Respondent-Appellant Banco Bilbao Vizcaya Argentaria, S.A. (“BBVA”) appeals from an August 2, 2018 final judgment of the U.S. District Court for the Southern District of New York (Hellerstein, J.) entered following issuance of our mandate in Vera v. Banco Bilbao Vizcaya Argentaria, S.A., 729 Fed. App’x 106 (2d Cir. 2018). As relevant here, the District Court’s judgment rendered final several of its previous orders requiring BBVA to turn over funds to Petitioners-Appellees Jeannette Fuller Hausler, Gustavo E. Villoldo, and Alfredo Villoldo from a blocked electronic fund transfer originated by the Cuban Import-Export Corporation, an instrumentality of the Republic of Cuba. These turnover orders, in turn, rested on the District Court’s grant of full faith and credit to default judgments that Petitioners-Appellees secured against Cuba in Florida state courts, whose jurisdiction against the sovereign was asserted under the state-sponsored terrorism exception of the Foreign Sovereign Immunities Act, 28 U.S.C. §1605A (“FSIA”). The District Court made no independent findings regarding its own jurisdiction to enforce these judgments under the FSIA, and in particular under section 201(a) of the Terrorism Risk Insurance Act, 28 U.S.C. §1610 note. Because our review of the record convinces us that jurisdiction did not lie, we reverse the judgment of the District Court, vacate the District Court’s turnover orders, and remand the cause with instructions to dismiss the action for lack of subject-matter jurisdiction. Applying common-law equitable principles of restitution, we further direct the District Court to order Petitioners-Appellees, as well as Plaintiff-Appellee Aldo Vera, Jr., also a party in these proceedings and a beneficiary of the same turnover orders, to return to BBVA the funds that BBVA paid them under the void turnover orders. REVERSED and REMANDED with instructions. JUDGE CABRANES joins the judgment of the Court. SUSAN CARNEY, C.J. This is the fifth appeal that we have seen in these proceedings. The current controversy arises from the efforts of Petitioners-Appellees Gustavo E. Villoldo and Alfredo Villoldo (“the Villoldos”) and Jeannette Fuller Hausler (collectively, “the Villoldos and Hausler” or “Petitioners”) to enforce several default judgments obtained by them against the Cuban government in Florida state courts. These judgments rest, factually, on allegations of torture and extrajudicial killing suffered by members of Petitioners’ families in 1959 and 1960 at the hands of the revolutionary Cuban state. They rest, legally, with respect to those courts’ jurisdiction over Cuba, on the state-sponsored terrorism exception of the Foreign Sovereign Immunities Act (“FSIA”), now codified at 28 U.S.C. §1605A, and earlier found in substantially the same form at 28 U.S.C. §1605(a)(7). Section 201(a) of the Terrorism Risk Insurance Act (“TRIA”), codified at 28 U.S.C. §1610 note, would provide the District Court here a jurisdictional basis for enforcing those state judgments, if valid, by attaching and executing on Cuban assets blocked by banking institutions under the Cuban Assets Control Regulations, 31 C.F.R. Part 515. Section 1605A revokes a state’s sovereign immunity from legal proceedings and liability for certain terrorism-related claims for personal injury and death if, in addition to meeting ordinary tort liability standards, “the foreign state was designated as a state sponsor of terrorism at the time [the tortious act] occurred, or was so designated as a result of such act.” 28 U.S.C. §1605A(a)(2)(A)(i)(I) (emphasis supplied). The Republic of Cuba (“Cuba”) was designated as a state sponsor of terrorism only in March 1982 — over two decades after the abhorrent conduct that Petitioners allege. Accordingly, courts may exercise jurisdiction over Petitioners’ claims against Cuba only if they can establish that either (1) Cuba was designated as a state sponsor of terrorism in 1982 at least in part because of the actions it took against their family members in 1959 and 1960, or (2) Cuba committed certain acts of terrorism (within the statute’s meaning) against Petitioners or their family members after 1982. Beginning in about 2007, Plaintiff-Appellee Aldo Vera, Jr. (“Vera”), the Villoldos, and Hausler (collectively, “Appellees”) independently pursued litigation on their tort claims in Florida state courts, each obtaining a significant default judgment against Cuba. (Hausler’s judgment was for over $400 million, Vera’s, for $95 million, and the Villoldos’, for $2.79 billion.) In 2013, seeking enforcement of those judgments in New York, they jointly filed an Omnibus Turnover Petition in the U.S. District Court for the Southern District of New York against nineteen banks. Those banks, Appellees alleged, held blocked Cuban assets in New York. One of the banks, Respondent-Appellant Banco Bilbao Vizcaya Argentaria, S.A. (“BBVA”), sought dismissal of the turnover petition, contending first that the District Court lacked subject-matter jurisdiction over the enforcement proceeding, and, then, in the alternative, that the Florida state court judgments were void and not entitled to the federal court’s full faith and credit. The District Court denied BBVA’s motion to dismiss but did not make a threshold jurisdictional determination in doing so, relying instead on the jurisdictional findings and legal conclusions of the three Florida state courts to proceed under TRIA section 201(a). As we held in reviewing (and vacating) a prior contempt order against BBVA issued by the District Court with respect to Vera, reliance on a state court’s legal conclusions does not adequately support a federal court’s own exercise of subjectmatter jurisdiction against a foreign sovereign or its assets when a proceeding is predicated on a default judgment. In Vera v. Republic of Cuba, 867 F.3d 310, 318 (2d Cir. 2017) (“Vera III”), we explained that the District Court was required to “analyze the record independently to determine if Cuba was immune” from its jurisdiction and that the Florida courts’ jurisdictional findings do not “bind or aid” it in making this determination. See Verlinden B.V. v. Cent. Bank of Nigeria, 461 U.S. 480, 493-94 (1983) (“At the threshold of every action in a District Court against a foreign state…it must apply the detailed federal law standards set forth in the Act.”). Accordingly, the District Court’s judgment against BBVA and the turnover orders that preceded it are subject to serious challenge. After carefully examining the record on appeal, we conclude that, had it independently determined the issue, the District Court would necessarily have found that Hausler and the Villoldos failed to establish that the exception to sovereign immunity provided for in section 1605A applied. As we ruled with respect to Vera in Vera III, Petitioners here have failed to show under section 1605A either that (1) Cuba was designated as a state sponsor of terrorism “as a result” of the pre-1982 acts underlying their judgments or that (2) the acts underlying their judgments occurred after 1982. Without either showing, the state-sponsored terrorism exception did not permit the court to exercise jurisdiction over Cuba’s assets under TRIA section 201(a). Accordingly, and as spelled out in greater detail below, we decide that the District Court did not have subject-matter jurisdiction over this enforcement proceeding. We therefore REVERSE the District Court’s judgment; VACATE the District Court’s turnover orders; and REMAND the cause to the District Court with instructions (1) to dismiss the amended Omnibus Turnover Petition and (2) to enter an order directing restitution by Appellees of the funds that BBVA paid them. BACKGROUND1 I. The start of the Vera proceedings The proceedings that culminated in this appeal began in March 2012, when Vera, who held a similar default judgment against Cuba issued by a Florida state court, filed suit in the U.S. District Court for the Southern District of New York seeking to enforce that judgment. Vera v. Republic of Cuba, No. 12-CV-1596 (S.D.N.Y.). In August 2012, after Cuba’s default in the federal proceeding, the District Court (Hellerstein, J.) determined that Vera’s Florida state court judgment was due full faith and credit and, accordingly, entered a federal judgment in the amount of approximately $49 million in Vera’s favor. Then, in late 2012 and early 2013, Vera filed numerous turnover motions, seeking to seize assets from banks in New York that he alleged to be holding Cuban assets. Vera was not long alone in seeking to enforce a default judgment against Cuba in New York federal courts. In 2013, both Hausler and the Villoldos — that is, Petitioners in this case — intervened in the Vera enforcement proceedings, asserting that their rights as judgment creditors were entitled to priority over Vera’s. Before reviewing what happened next in those proceedings, it will be helpful to describe the key facts underlying the Villoldo and Hausler state court judgments and to provide a short outline of their respective procedural histories.2 II. The Villoldo judgment Gustavo E. Villoldo (“Gustavo”) and Alfredo Villoldo (“Alfredo”) are the Cubanborn sons of the late Gustavo Villoldo Argilagos (“Villoldo Argilagos”). Their father, a dual citizen of the U.S. and Cuba, founded a successful automotive company and owned numerous other businesses and landholdings in Cuba before the Cuban Revolution. After the revolution brought the Castro government to power on January 1, 1959, the Villoldo family became a target of the new regime because of their financial wealth and ties to the United States. Both sons are U.S. citizens. Cuban soldiers arrested Gustavo and Alfredo on January 6, 1959. Gustavo was detained in unhealthy and inhumane conditions, beaten, and interrogated under torture in a Cuban facility where executions were being carried out. After their release five days later, the brothers and their father continued to be subject to severe harassment by the Cuban government. Cuban soldiers repeatedly took Villoldo Argilagos into custody and threatened to murder the entire family unless he turned over the family’s businesses and properties to the new regime. On February 16, 1959, one day after meeting with prominent Cuban government member Ernesto “Che” Guevara, Villoldo Argilagos committed suicide. He did so, according to Gustavo’s testimony, because he was ordered to do so to save the lives of his wife and sons. The two brothers then fled to the United States, leaving behind their family’s vast properties, which were soon after confiscated. After leaving Cuba, Gustavo Villoldo joined the Central Intelligence Agency, and engaged in important intelligence activities on behalf of the United States. These included the 1967 operation that led to Che Guevara’s execution in Bolivia. In deposition testimony, Gustavo Villoldo recounted that, shortly after the operation, two Cuban agents were sent to New York to kidnap or kill him. He testified further in general terms that, between 1997 and 2003, when he was living in the United States, the Cuban government made numerous threats against his life. In August 2011, in a Florida state court proceeding, the Villoldo brothers secured a default judgment against Cuba for these wrongs. The court entered judgment in their favor in the amount of $2.79 billion, denominating $1 billion of that sum as punitive damages.3 The Florida state court characterized Cuba’s actions against the Villoldo family as “torture” within the meaning of section 1605A of title 28 and ruled that, under that section, it had subject-matter jurisdiction to hear their claims. In December 2011, the Villoldos sued Cuba in the U.S. District Court for the Southern District of New York, seeking recognition and enforcement of their Florida judgment under the Full Faith and Credit Act, 28 U.S.C. §1738. Villoldo v. Castro Ruz, No. 11-CV-9394 (S.D.N.Y.) (Swain, J.). In October 2012, according full faith and credit to the Florida judgment, Judge Swain entered a default judgment against Cuba and related individuals and entities in that case in the sum awarded by the Florida state court, making no independent jurisdictional findings. In November 2017, after their ongoing enforcement proceedings in the District Court were nearly complete, the Villoldos (having returned to Florida state court) filed a “motion to re-establish the court record” there with respect to the 2011 judgment. They submitted new affidavits from Gustavo Villoldo, his daughter Elia Lora, and his attorney Andrew C. Hall, and various attachments to those affidavits. Granting this motion, the Florida state court then ruled — in November 2017 — that “the information contained within the affidavits and attachments were relied upon by the Court when rendering its verdict at trial [in 2011] in this case.” J. App’x 1027. Citing this newly-submitted evidence, the Florida court issued an opinion and amended final judgment on June 4, 2018, making significant additional findings of fact and instructing that the judgment was effective nunc pro tunc as of August 19, 2011. In their 2017 affidavits, Gustavo Villoldo and Elia Lora represented that they had earlier testified at trial that their home in Florida was once surrounded by armed men whom they perceived to be agents of the Cuban state.4 Lora’s affidavit reflects that she had observed four men with large guns in their hands, that her family members armed themselves with two AR-15 rifles and yelled at the intruders to leave, and that local police responded to their 911 call within minutes but could not find the intruders. Neither Alfredo nor Gustavo Villoldo was present in the home at the time. More broadly, Gustavo Villoldo averred that he was subjected to a “concerted and continuing effort” by Cuba following Che Guevara’s death in 1967 “to locate [him] in order to carry out [his] assassination.” J. App’x 882. III. The Hausler judgment Jeannette Fuller Hausler (now deceased) was a U.S. citizen.5 Her brother, Robert Otis Fuller, nicknamed “Bobby,” was a dual U.S.-Cuban national born in Cuba, and heir to significant Cuban agricultural and business holdings. Mirroring the Villoldos’ experience, the Fuller family’s lives and properties were threatened by the new Cuban regime after January 1959. In early October 1960, Cuban agents arrested Fuller, who was returning from a short trip to Miami, and charged him with engaging in counterrevolutionary activities. He was tortured until he signed a prepared confession. Fuller was then presented to a military tribunal where, within minutes, he was tried and sentenced to death. In the proceedings, he was denied access to meaningful legal counsel and was not permitted to call witnesses in his defense. On October 16, 1960, he was executed by firing squad. His death prompted the U.S. Department of State to file a formal protest denouncing the proceedings. In the protest, the Department accused the Cuban authorities of carrying out Fuller’s trial in a “Roman [c]ircus atmosphere,” failing to “observe basic civilized standards,” and engaging in “inhuman behavior.” J. App’x 597-98. In January 2007, in Florida state court, Hausler secured a default judgment against Cuba for $400 million, of which $300 million was designated as punitive and $100 million as compensatory damages. In an opinion accompanying the judgment, the Florida state court ruled that Fuller was a victim of “extra-judicial killing” and asserted jurisdiction over Cuba under the FSIA’s state-sponsored terrorism exception, then codified at 28 U.S.C. §1605(a)(7).6 J. App’x 592. The following year, on Hausler’s application, the U.S. District Court for the Southern District of Florida granted full faith and credit to the state court judgment and entered a default judgment against Cuba, making no independent jurisdictional findings. Hausler v. Republic of Cuba, No. 08-CV-20197 (S.D. Fla.) (Jordan, J.). Hausler then began proceedings in the Southern District of New York. Hausler v. Republic of Cuba, No. 09-CV-10289 (S.D.N.Y.) (Marrero, J.). In 2009 and 2010, relying on the Florida state and federal judgments, Hausler served writs of garnishment against various New York banks holding blocked Cuban assets. She then formally intervened in the Vera enforcement proceedings, now before us on appeal. IV. The Vera enforcement proceedings The proceedings leading to this appeal have been protracted and circuitous, to say the least. As previewed in Section I, supra, Hausler and the Villoldos sought to use their Florida state court judgments to seize Cuban assets held by banks operating in the Southern District of New York. In 2013, both intervened in the Vera proceedings. Between March and June of that year, the Villoldos opposed Vera’s turnover motions, contending that Vera’s Florida state court judgment was void for lack of subject-matter jurisdiction and asserting, inter alia, that Aldo Vera, Sr., the victim of Cuba’s acts, was not a U.S. national and was not actually killed by agents of Cuba, but rather by criminal elements operating in Puerto Rico.7 In May 2013, Hausler intervened, contending that her rights as a judgment creditor preceded and therefore should take priority over those of both Vera and the Villoldos. After this initial period of competition, however, the three family groups reached a détente. They advised the District Court that they would jointly petition for turnover of the relevant assets. In September 2013, they did so, filing the Omnibus Petition for Turnover Order (“Omnibus Petition”) that we have mentioned and naming as respondents BBVA and eighteen other banks which, they alleged, were holding blocked Cuban assets.8 BBVA moved to dismiss the Omnibus Petition for lack of subject-matter jurisdiction. The District Court denied the motion, construing BBVA’s motion as a collateral attack on the Florida state court judgments, and not as a challenge to its own jurisdiction. In rejecting BBVA’s arguments, the District Court commented that “[BBVA] must concede that the Florida [courts] made appropriate jurisdictional findings, and created a sufficient evidentiary record.” Vera v. Republic of Cuba, 40 F. Supp. 3d 367, 376 (S.D.N.Y. 2014). The court further interpreted BBVA’s motion as an improper challenge to the “merits” of the Florida state courts’ determinations in that it attacked the Florida courts’ findings (in the District Court’s words) “that Cuba was designated as a state sponsor of terrorism, at least partially, as a result of the acts against Villoldo, Hausler, and Vera.” Id. This “merits” argument was impermissible, in the District Court’s view, because the Florida courts “held a trial in each of the three cases, found the facts, and applied the law, finding that acts of terrorism took the lives of plaintiffs’ family members [and] that Cuba was designated as a state sponsor of terrorism either before these acts or partially as a result of these acts.” Id.9 Determining then that it had jurisdiction to proceed, the District Court entered two orders important to the resolution of the appeal before us. In September 2014, the court enforced a subpoena in which Vera sought information about BBVA’s holdings of Cuban assets outside the United States. Then, in March 2015, the District Court ordered that BBVA turn over the contents of a certain account to the U.S. Marshal. That account contained $553,185.21, the proceeds of an electronic fund transfer (“EFT”) that had been initiated by the Cuban Import-Export Corporation, a Cuban instrumentality.10 Vera v. Republic of Cuba, 91 F. Supp. 3d 561, 573 (S.D.N.Y. 2015). BBVA timely appealed both of these orders, but we were compelled to dismiss its appeals for lack of jurisdiction because neither the order enforcing Vera’s subpoena nor the turnover orders were “final decisions” of the District Court appealable under 28 U.S.C. §1291. See Vera v. Republic of Cuba, 802 F.3d 242, 246 (2d Cir. 2015) (“Vera I”) (subpoena enforcement order not appealable); Vera v. Republic of Cuba, 651 Fed. App’x 22, 26 (2d Cir. 2016) (“Vera II”) (turnover orders not appealable). After our decision in Vera I, BBVA refused to produce any information in response to the subpoena, and, upon the parties’ stipulation to that effect, the District Court held BBVA in contempt in April 2016. BBVA appealed the contempt order, this time secure in its expectation of appellate jurisdiction. See In re Air Crash at Belle Harbor, 490 F.3d 99, 104 (2d Cir. 2007) (contempt orders regarded as final and appealable). In May 2017, while its appeal from the contempt order was pending, the District Court denied BBVA’s motion for a further stay and ordered that the funds seized from BBVA be turned over to Appellees collectively.11 Vera v. Republic of Cuba, No. 12-CV-1596 (AKH), 2017 WL 4350568, at *3 (S.D.N.Y. May 25, 2017). In adjudicating BBVA’s appeal from the District Court’s contempt order, we held that the District Court lacked subject-matter jurisdiction over Vera’s enforcement action against Cuba altogether; therefore, both the subpoena served by Vera on BBVA to enforce his judgment and the subsequent contempt order were void. Vera v. Republic of Cuba, 867 F.3d 310, 321 (2d Cir. 2017) (“Vera III”). Because Vera III concerned a discovery dispute pertaining only to Vera, however, the question whether the District Court had subject-matter jurisdiction to enforce the judgments held by Hausler and the Villoldos was not before us. In line with our mandate in Vera III, the District Court vacated the judgment it issued as to Vera, quashed Vera’s subpoena, and vacated the related contempt order. It took no action with respect to Hausler and the Villoldos. BBVA then appealed the District Court’s May 2017 order directing that the funds be disbursed jointly to the three cooperating sets of plaintiffs, and we once again dismissed its appeal of the non-final order for lack of appellate jurisdiction. Vera v. Banco Bilbao Vizcaya Argentaria, S.A., 729 Fed. App’x 106 (2d Cir. 2018) (“Vera IV”). This time, however, we directed the District Court “to issue an appealable final judgment expeditiously” on remand so as to facilitate prompt review. Id. at 108. In accordance with our mandate in Vera IV, the District Court entered final judgment on August 2, 2018. BBVA timely appealed. Now, on this matter’s fifth trip to this Court,12 our appellate jurisdiction over the entirety of the dispute between BBVA, on one hand, and Hausler, the Villoldos, and Vera, on the other, is undisputed. DISCUSSION To resolve this appeal, we must address several intertwined factual and legal issues. We begin by reviewing the general principles of sovereign immunity as they apply to terrorism claims brought against a foreign state. Following Vera III, we next stress that, when a district court is presented with a default judgment against a foreign sovereign, it must assure itself of its own power to hear the case without relying on the jurisdictional findings and legal conclusions of the court that issued the judgment. Then applying this framework to the case at hand, we consider whether Petitioners have presented sufficient competent evidence that the 1982 designation of Cuba as a foreign sponsor of terrorism was linked, even in part, to its acts against Hausler and the Villoldos, to support the District Court’s exercise of jurisdiction over Cuba’s assets under TRIA section 201(a). After conducting a de novo review of the extensive record, we answer this question in the negative. We therefore conclude that the District Court lacked jurisdiction over Hausler and the Villoldos’ actions to enforce their judgments (just as it lacked jurisdiction over Vera’s action, the key question resolved in Vera III). We finish by considering whether in our discretion to order that Appellees make restitution of the funds collected by them as a product of the District Court’s jurisdictionally void orders. We conclude that such an order of restitution is appropriate in the circumstances presented here. I. Subject-matter jurisdiction over these claims against Cuba A. Principles of subject-matter jurisdiction under the Foreign Sovereign Immunities Act The Foreign Sovereign Immunities Act of 1976, Pub. L. 94-583, 90 Stat. 2891, governs the jurisdiction of courts in the United States over all private civil actions against foreign sovereigns.13 The FSIA provides the “sole basis for obtaining jurisdiction over a foreign state in our courts,” Argentine Republic v. Amerada Hess Shipping Corp., 488 U.S. 428, 434 (1989), and “must be applied by the District Courts in every action against a foreign sovereign,” Verlinden B.V., 461 U.S. at 493. See also Mobil Cerro Negro, Ltd. v. Bolivarian Republic of Venezuela, 863 F.3d 96, 113 (2d Cir. 2017) (referring to “[t]he Supreme Court’s emphatic and oft-repeated declaration in Amerada Hess” and collecting cases concerning the categorical nature of the FSIA). It codifies two types of foreign sovereign immunity — immunity from jurisdiction and immunity from attachment and execution of the sovereign’s property. We start by briefly describing the latter, as it is most directly at issue in this action to enforce Petitioners’ default judgments The FSIA provides that “the property in the United States of a foreign state shall be immune from attachment[,] arrest and execution except as provided in sections 1610 and 1611 of this chapter.” 28 U.S.C. §1609. In this case, the District Court asserted jurisdiction over the enforcement actions against Cuban assets under a modification to the FSIA enacted by TRIA section 201(a).14 That statute grants courts subject-matter jurisdiction over post-judgment execution and attachment proceedings involving blocked assets “in every case in which a person has obtained a judgment against a terrorist party on a claim based upon an act of terrorism, or for which a terrorist party is not immune under section 1605A or 1605(a)(7).”15 TRIA section 201(a) provides for federal court jurisdiction over execution and attachment proceedings involving the assets of a foreign sovereign, however, only where “a valid judgment has been entered” against the sovereign. Vera III, 867 F.3d at 321 (internal quotation marks omitted) (emphasis in original)). In other words, section 201 “provides jurisdiction for execution and attachment proceedings to satisfy a judgment for which there was original jurisdiction under the FSIA…if certain statutory elements are satisfied.” Weinstein v. Islamic Republic of Iran, 609 F.3d 43, 52 (2d Cir. 2010). Whether the District Court here had jurisdiction under TRIA to attach and execute on Cuba’s assets, therefore, turns on whether Petitioners held judgments that were based on an exception to immunity from jurisdiction established by the FSIA.16 Accordingly, we now look at the FSIA’s framework for sovereign immunity from jurisdiction. The FSIA establishes that “a foreign state [is] immune from the jurisdiction of the courts of the United States and of the States except as provided in sections 1605 to 1607 of this chapter.” 28 U.S.C. §1604. If any of the listed exceptions applies, however, then a court may exercise jurisdiction over the state, see 28 U.S.C. §1330(a), and the foreign state may be held liable, in state or federal court, “in the same manner and to the same extent as a private individual under like circumstances.” Id. §1606. In this case, the only jurisdictional exception relied on by Petitioners is section 1605A, known as the “state-sponsored terrorism exception” or the “terrorism exception” from sovereign immunity. First enacted in 1996,17 this section currently provides in relevant part A foreign state shall not be immune from the jurisdiction of courts of the United States or of the States in any case not otherwise covered by this chapter in which money damages are sought against a foreign state for personal injury or death that was caused by an act of torture, extrajudicial killing, aircraft sabotage, hostage taking, or the provision of material support or resources for such an act if such act or provision of material support or resources is engaged in by an official, employee, or agent of such foreign state while acting within the scope of his or her office, employment, or agency. 28 U.S.C. §1605A(a)(1). By its terms, this provision applies to claims for personal injury or death only if caused by one of several acts listed by statute: as relevant here, extrajudicial killing or torture. The exception is further cabined by two important preconditions set forth in subsection (a)(2). First, a court may hear such a claim only if “the foreign state was designated as a state sponsor of terrorism at the time the act described in paragraph (1) occurred, or was so designated as a result of such act.” Id. §1605A(a)(2)(A)(i)(I).18 Second, to maintain such a claim, either the claimant or the victim must be a U.S. national, member of the U.S. armed forces, or employee or contractor of the U.S. government at the time of the act giving rise to liability.19 Id. §1605A(a)(2)(A)(ii). Our Court has repeatedly held that both of these conditions must be satisfied for the terrorism exception to apply. See Vera III, 867 F.3d at 317 (“Even if a foreign state has engaged in one of the terrorist acts described above…it is not subject to suit in the United States unless the foreign state was designated as a state sponsor of terrorism [in accordance with the statute].” (internal quotation marks omitted)); In re Terrorist Attacks on Sept. 11, 2001, 714 F.3d 109, 115 n.7 (2d Cir. 2013) (“The FSIA’s terrorism exception…does not apply to [instrumentalities of a non-designated state] because that exception is only available against a nation that has been designated by the United States government as a state sponsor of terrorism at the time of, or due to, a terrorist act.”). Cuba never appeared in the Florida state court or the District Court here to present a defense, jurisdictional or otherwise. Nevertheless, “the FSIA, by its terms, authorizes consideration of sovereign immunity from both jurisdiction and execution even in the absence of an appearance by the sovereign.” Walters v. Indus. & Commercial Bank of China, Ltd., 651 F.3d 280, 293 (2d Cir. 2011). The statute allows for courts to “consider the [jurisdictional] issue once it is suggested by any party — or for that matter, non-party.” Id. (emphasis in original). Indeed, even if no party raises the issue, courts have an obligation to consider subject matter jurisdiction sua sponte. Henderson ex rel. Henderson v. Shinseki, 562 U.S. 428, 434 (2011). Accordingly, BBVA was entitled to raise Cuba’s sovereign immunity from execution on its assets before the District Court as a defense to Petitioners’ enforcement action; and it may, on appeal, challenge the District Court’s ruling that Cuba was not immune.20 B. Review and enforcement of default judgments in the FSIA context In reviewing a default judgment, we generally “deem[] all the well-pleaded allegations [as to liability] in the pleadings to be admitted.” Transatlantic Marine Claims Agency, Inc. v. Ace Shipping Corp., 109 F.3d 105, 108 (2d Cir. 1997). This principle does not preclude us, however, from undertaking “an inquiry into whether the default judgment itself is void for lack of subject matter jurisdiction.” Id. Pursuing such an inquiry, we review jurisdictional conclusions de novo, and in assessing “whether there is a factual basis to support the [District Court's] exercise of subject matter jurisdiction…we are not limited in our right to refer to any material in the record.” Velez v. Sanchez, 693 F.3d 308, 314 (2d Cir. 2012) (internal quotation marks omitted). In these proceedings, Petitioners asked the District Court to enforce judgments issued by several Florida state courts, each of which concluded that its jurisdiction over Cuba was authorized by the state-sponsored terrorism exception. These judgments did not, however, bar the District Court from considering the jurisdictional question anew, nor did they relieve it of its obligation to assure itself of its own jurisdiction, whether upon BBVA’s motion or sua sponte. It is generally true, of course, that “principles of res judicata apply to jurisdictional determinations — both subject matter and personal.” Ins. Corp. of Ireland, Ltd. v. Compagnie des Bauxites de Guinee, 456 U.S. 694, 702 n.9 (1982). At the same time, a finding of jurisdiction is preclusive only when the jurisdictional issues “have been fully and fairly litigated…in the court which rendered the original judgment.” Durfee v. Duke, 375 U.S. 106, 111 (1963). Here, as we decided in Vera III, Cuba’s failure to appear meant that, although the Florida courts heard relevant evidence, “the jurisdictional facts necessary to eliminate Cuba’s sovereign immunity under the FSIA were not fully and fairly litigated” in the Florida actions. 867 F.3d at 318. The Florida state courts’ jurisdictional conclusions could therefore “neither bind the District Court…nor…be relied on by the parties.” Id; see also Jerez v. Republic of Cuba, 775 F.3d 419, 422-23 (D.C. Cir. 2014) (refusing to accord res judicata effect to similar Florida state default judgment entered against Cuba). Thus, to determine whether it had jurisdiction under TRIA section 201(a) to attach or execute on Cuba’s assets, the District Court should have first determined for itself whether the state-sponsored terrorism exception to jurisdictional immunity applied to the Florida state court default judgments.21 See Vera III, 867 F.3d at 321 (in absence of valid underlying judgment, “TRIA did not provide a proper basis for subject matter jurisdiction over subsequent proceedings”). In this case, however, the District Court simply granted full faith and credit to the Florida courts’ jurisdictional conclusions rather than analyzing whether their determinations could support its application of the terrorism exception. See Vera, 40 F. Supp. 3d at 376-77. This deficiency calls into question the District Court’s exercise of jurisdiction over the enforcement of the judgments. Ordinarily, we would address a District Court’s failure to make appropriate findings to support its jurisdiction by remanding for further proceedings. In Vera III, however, we declined to do so because “the case present[ed] no relevant unanswered factual issues regarding the existence of subject matter jurisdiction.” 867 F.3d at 319 n.8. We follow the same approach here and proceed to decide de novo whether the District Court had subject-matter jurisdiction under the FSIA and TRIA section 201(a) over the enforcement actions brought by Hausler and the Villoldos.22 C. The Villoldos’ and Hausler’s claims and Cuba’s designation as a state sponsor of terrorism The Villoldos’ and Hausler’s claims arise largely from acts that predated Cuba’s 1982 designation as a state sponsor of terrorism by over two decades. Accordingly, to justify invoking those pre-1982 acts and the state-sponsored terrorism exception to sovereign immunity as the basis for this enforcement action, they must establish that Cuba was so designated “as a result of” its acts against their families. See 28 U.S.C. §1605A(a)(2)(A)(i)(I); see also id. §1605(a)(7)(A) (2007); City of New York v. Permanent Mission of India to the United Nations, 446 F.3d 365, 369 (2d Cir. 2006) (“The party seeking to establish jurisdiction [over a foreign state] bears the burden of producing evidence establishing that a specific exception to immunity applies.”). We have not yet had occasion to articulate how taut the causal link must be between a specific enumerated act — such as an extrajudicial killing or act of torture — and a country’s later designation to support application of the terrorism exception. Here too, we need not address whether Petitioners must meet the more demanding standard of “but-for causation” (i.e., that Cuba was designated a state sponsor of terrorism as a direct result of the specific acts taken against their family members, and that it would not otherwise have been so designated). Rather, as we did in Vera III, we examine the record to ascertain if the Villoldos or Hausler adduced evidence that “specifically links” Cuba’s acts against their families to the Secretary of State’s determination in 1982 to designate Cuba as a state sponsor of terrorism. 867 F.3d at 319. And again, as in Vera III, we find the record patently insufficient, even under this lesser causation standard, to support the Villoldos’ and Hausler’s position. During one of several collateral federal district court proceedings spawned by this sprawling litigation, the State Department in 2012 filed a Statement of Interest presenting its formal position as to the “reason or reasons Cuba was designated a state sponsor of terrorism under Section 6(j) of the Export Administration Act of 1979.”23 J. App’x 323. The submission, which BBVA points to on appeal, consisted of an affidavit by Peter M. Brennan, an experienced diplomat who was then in charge of the Department’s Office of the Coordinator for Cuban Affairs. Brennan averred that, in 1982, when it was so designated, “Cuba belonged in the category of states that have repeatedly provided support for…organizations and groups abroad that used terrorism and revolutionary violence as a policy instrument to undermine existing governments.” Id. at 324. This support was the reason for its designation, he implied. In support of this understanding, Brennan’s affidavit cited contemporaneous Congressional testimony given by two State Department officials: (1) the March 12, 1982 testimony of Thomas Enders, Assistant Secretary of State for Inter-American Affairs, before the Subcommittee on Security and Terrorism of the Senate Judiciary Committee; and (2) the March 18, 1982 testimony of Ernest Johnson, Jr., Deputy Assistant Secretary for Economic Affairs, before a subcommittee of the Senate Foreign Relations Committee.24 We also referred to these documents in Vera III. Enders, in his testimony before the Senate Subcommittee on Security and Terrorism, provided an extensive catalogue of Cuban support given to insurgent groups in other Latin American countries, including Nicaragua, El Salvador, Guatemala, Honduras, Costa Rica, Colombia, and Chile. Enders specifically referenced Cuba’s implementation in 1978 of a “new strategy…of uniting the left in the countries of the hemisphere for the purpose of using it…[to establish] more Marxist-Leninist regimes in this hemisphere” as standing in contrast to the country’s previous attempts to “portray itself as a member of the international community not unlike others, carrying out state-to-state relations through embassies and emphasizing trade and cultural contacts.” J. App’x 332. Enders portrayed the members of the Cuban leadership group as subject to a “deep-seated drive to re-create their own guerrilla experience elsewhere,” observing that “the Castro regime has made a business of violent revolution.” Id. at 336. Johnson’s brief testimony echoed Enders’s remarks. He again tied Cuba’s 1982 designation to its support of armed groups outside its borders. He expressed the “hope [that]…the addition of Cuba [to the list] will demonstrate to other countries…that our export controls are truly directed towards terrorism…. In the case of Cuba, we evaluated carefully the evidence of Cuban support for revolutionary violence and groups that use terrorism as a policy instrument.” Id. at 362. Notably absent from Enders’s and Johnson’s testimony is any reference to political repression or human rights abuses within Cuba itself, either during the 1959-60 period, when Cuba tortured the Villoldos and their father and executed Bobby Fuller; during the period immediately preceding Cuba’s 1982 designation as a state sponsor of terrorism; or in any other time period. Instead, the underlying record supports Brennan’s assertion that Cuba was designated as a result of its “support for organizations and groups abroad that used terrorism and revolutionary violence as a policy instrument.” J. App’x at 324; see also Vera III, 867 F.3d at 318 (reaching same conclusion). In the face of these official statements describing the Secretary of State’s reasons in 1982 for designating Cuba as a state sponsor of terrorism, neither the Villoldos nor Hausler present any persuasive evidence that Cuba was in fact so designated “as a result of” its violent actions against their families decades prior. The Villoldos The Villoldos cite extensively the jurisdictional conclusions of the Florida state court. Such conclusions, however, cannot be relied on by the parties to establish jurisdiction in the District Court here. Vera III, 867 F.3d at 318. They also recount their allegations of horrible mistreatment that they and their father suffered at the hands of the Cuban revolutionary government in 1959, but provide no evidence that might “specifically link” these acts to the Secretary of State’s 1982 designation of Cuba as a state sponsor of terrorism. Looking to other acts to establish such a link, the Villoldos refer further to the Florida state court’s factual finding that “Cuba stole [their family's] enormous wealth and used it to fund the exportation of terrorism throughout Latin America, establishing jurisdiction as to all three Villoldo plaintiffs.” Villoldo Br. 49. But, even assuming that Cuba’s seizure of the Villoldos’ assets helped to support its later promotion of terrorism overseas, the available record strongly suggests that Cuba was not designated a state sponsor of terrorism as a result of any seizure of assets within its borders, regardless of the use to which it later may have put some portion of those assets. Accordingly, the Villoldos have failed to meet their burden to establish that the District Court had jurisdiction over their action to enforce their Florida state judgment based on Cuba’s acts of torture or property seizures committed in 1959. Turning to more recent events, the Villoldos contend in the alternative that the District Court here had jurisdiction to enforce their state court judgment because of Cuba’s alleged repeated attempts to assassinate Gustavo Villoldo after its 1982 designation as a state sponsor of terrorism. These, they insist, constituted some of the acts of “torture” on which the Florida state judgment was based.25 Villoldo Br. 49-52. Their allegations, however, are legally insufficient. The terrorism exception incorporates the definition of “torture” established in the Torture Victim Protection Act of 1991 (“TVPA”), Pub. L. No. 102-256, 106 Stat. 73. See 28 U.S.C. §1605A(h)(7). The TVPA defines torture as “any act, directed against an individual in the offender’s custody or physical control, by which severe pain or suffering…whether physical or mental, is intentionally inflicted on that individual for [certain enumerated purposes].” 28 U.S.C. §1350 note (emphasis added). See Chowdhury v. Worldtel Bangladesh Holding, Ltd., 746 F.3d 42, 52 (2d Cir. 2014) (torture is a “deliberate and calculated act of an extremely cruel and inhuman nature specifically intended to inflict excruciating and agonizing physical or mental pain or suffering”) (citation omitted). The Villoldos urge, and the Florida state court reached the legal conclusion, that “threats of assassination and assassination attempts” carried out against Gustavo Villoldo after 1982 “are properly classified as torture.” J. App’x 865. After reviewing the record, we conclude that neither the Florida court’s findings of fact nor any evidence submitted by the Villoldos — nor, indeed, the Villoldos’ general allegations — support this conclusion.26 Accordingly, the Villoldos failed to establish that Cuba committed torture or any other act enumerated in section 1605A(a)(1) against either of them after 1982. The District Court therefore lacked jurisdiction over the Villoldos’ enforcement action and should have dismissed their petition.27 Hausler For her part, Hausler seeks to satisfy the preconditions to reliance on the terrorism exception by pointing to testimony given by Peter Deutsch, a former Congressman, and Jaime Suchlicki, a professor at the University of Miami and expert on Cuban affairs.28 Deutsch testified in a 2003 deposition in unrelated proceedings that, as a member of Congress, he was a cosponsor of the 1996 AEDPA amendment that generated the terrorism exception. In that deposition, he stated his view that “in 1961 President Kennedy effectively and in fact…designated [Cuba] as a state sponsor of terrorism.” J. App’x 685. In a 2012 affidavit filed in related proceedings in the U.S. District Court for the Southern District of Florida, Deutsch further declared that he “agreed to be directly involved in the drafting and enactment as a co-sponsor of the [FSIA terrorism exception] based upon assurances that my constituents who had suffered from the Government of Cuba’s acts of extra-judicial killing and torture during the period of 1960-61 would, under this legislation, be able to obtain legal redress.” Id. at 661. He emphasized that he “would not have agreed to be a co-sponsor of that legislation [had he] not received those assurances,” and that he “was assured that the language as drafted, and as later enacted, met this test.” Id. In 2012, Deutsch reiterated his view that “[i]n 1961 President John F. Kennedy effectively and in fact designated the Government of Cuba a state sponsor of terrorism, in part by reason of the extra-judicial killing of U.S. citizens during the 1960-61 time period.” Id. at 662. Professor Suchlicki supported Deutsch’s assertions. He averred in a 2012 affidavit that the “historical evidence overwhelmingly demonstrates that the Government of Cuba was condemned by the Kennedy administration starting no later than early 1961, based at least in part upon the extrajudicial killing and torture of U.S. citizens,” and that, as a professional in the field, he was “not aware of any statement which would support the view that support for Latin American revolutionaries was the only reason for such designation of the Government of Cuba as a state sponsor of terrorism.” Id. at 673. The assessments offered in the statements of Deutsch and Suchlicki reflect a misunderstanding of the statutory regime that governs sovereign immunity and its “terrorism exception.” The version of FSIA in effect when Hausler obtained her judgment abrogated the sovereign immunity of a foreign state designated under “section 6(j) of the Export Administration Act of 1979 (50 U.S.C. App. 2405(j)) or section 620A of the Foreign Assistance Act of 1961 (22 U.S.C. 2371).” 28 U.S.C. §1605(a)(7)(A) (2007). Congress did not, however, add section 620A to the Foreign Assistance Act until June of 1976. Pub. L. No. 94-329, §303, 90 Stat. 729 (1976). Cuba could not therefore have been so designated in 1961 as Deutsch and Suchlicki appear to claim. Deutsch and Suchlicki, however, are not entirely incorrect. Section 620(a) of the original Foreign Assistance Act of 1961 expressly prohibited the provision of foreign aid to Cuba and authorized the President “to establish and maintain a total embargo upon all trade between the United States and Cuba.” Pub. L. No. 87-195, §620, 75 Stat. 424, 444-45 (1961). Moreover, President Kennedy in fact implemented such an embargo in February 1962. Proclamation No. 3447, Embargo on All Trade with Cuba, 27 Fed. Reg. 1085 (Feb. 7, 1962). Thus, while Deutsch and Suchlicki are correct that President Kennedy sanctioned Cuba during this period (and he did so under a provision of the Foreign Assistance Act adjacent to that identified in the FSIA), these sanctions did not lift Cuba’s immunity under the FSIA. Accordingly, as demonstrated by the previously cited Congressional testimony of high-ranking State Department officials, Cuba was not designated as a state sponsor of terror under the relevant provisions until 1982. Because the decision to designate a state as a sponsor of terrorism is committed by statute to the discretion of the Secretary of State, we often regard such official pronouncements as authoritative.29 See Vera III, 867 F.3d at 319 (relying on “legislative materials and statements by government officials submitted in this case [that] make no mention of extrajudicial killings or of the death of Vera’s father”); Roeder v. Islamic Republic of Iran, 195 F. Supp. 2d 140, 160-61 (D.D.C. 2002) (relying on State Department reports and letters to conclude that Iran was not designated as a state sponsor of terrorism as a result of the 1979-81 hostage crisis and rejecting contrary testimony given by an independent expert), aff’d, 333 F.3d 228 (D.C. Cir. 2003). In sum, although Hausler’s witnesses establish that a succession of presidential administrations has vigorously condemned human rights abuses in Cuba, Hausler cannot seriously dispute that it was not until 1982 that Cuba was designated a state sponsor of terrorism, and that the record shows that the basis for the formal designation was Cuba’s active support for violent groups acting outside of its borders. See Vera III, 867 F.3d at 318. Thus, Hausler, too, failed to adduce evidence demonstrating a specific link between the death of her brother in 1960 and Cuba’s designation as a state sponsor of terrorism over two decades later. Accordingly, she has failed to meet her burden to establish that the District Court had jurisdiction over her action under TRIA section 201(a) to enforce her Florida state court judgment. We conclude, therefore, that the terrorism exception — the sole potential basis for subject-matter jurisdiction in this case — applied neither to Hausler nor the Villoldos’ actions before the District Court. Hausler and the Villoldos thus did not hold valid judgments against Cuba enforceable under TRIA section 201(a); the District Court lacked jurisdiction over the enforcement proceeding; and the District Court’s orders requiring BBVA and other banks to turn over blocked Cuban assets to all three groups of Appellees (Hausler, the Villoldos, and Vera) were void for want of jurisdiction. II. Restitution of funds turned over to Appellees Having determined that the District Court lacked subject-matter jurisdiction over the Villoldo and Hausler enforcement actions — and having earlier decided the same with respect to Vera in Vera III — we now confront the consequences of these rulings. The District Court declined to stay execution of its turnover orders pending BBVA’s appeal from the court’s final judgment. For the reasons set forth above, we conclude that these turnover orders were void ab initio. BBVA has requested that, if such a result is reached, this Court order all three Appellees to make restitution to BBVA of the funds that they received under the invalid turnover orders. Appellees counter that restitution to BBVA is inappropriate because BBVA lacks its own possessory interest in the funds. After all, Appellees argue, the funds at issue are the property of the Cuban Import-Export Corporation, a Cuban instrumentality that never appeared in this case; BBVA was merely an intermediary bank that blocked the assets under the Cuban Assets Control Regulations, 31 C.F.R. Part 515. Accordingly, Appellees urge, once BBVA delivered the funds to the Registry of the U.S. Courts, it was dispossessed of any interest of its own, and only the Cuban Import-Export Corporation or the Cuban government itself would have standing to seek their return. To this, BBVA replies that it retains a possessory interest in the funds because (1) it is subject to potential liability for the funds to the Cuban corporation; and (2) it is entitled to an equitable lien on the monies for its expenses in diligently protecting the Cuban corporation’s property from execution. In considering what equity demands in this situation, we first summarize the traditional standards applicable to requests for restitution and then consider their application here. The Supreme Court has long ago observed that “[t]he right to recover what one has lost by the enforcement of a judgment subsequently reversed is well established.” Baltimore & O.R. Co. v. United States, 279 U.S. 781, 786 (1929). This well-established right may be tempered, however, by application of equitable principles. Thus, the most recent Restatement of the law of restitution offers this qualified statement: “A transfer or taking of property, in compliance with or otherwise in consequence of a judgment that is subsequently reversed or avoided, gives the disadvantaged party a claim in restitution as necessary to avoid unjust enrichment.” Restatement (Third) of Restitution and Unjust Enrichment §18 (Am. Law Inst. 2011) (emphasis added). Because an order of restitution is generally seen as discretionary, we consider whether “the money was received in such circumstances that the possessor will give offense to equity and good conscience if permitted to retain it.” Atl. Coast Line R. Co. v. Florida, 295 U.S. 301, 309 (1935). In conducting this inquiry, we are mindful of the Restatement’s comment that a judgment debtor’s “entitlement to restitution may not be resisted merely on the ground that an invalid judgment gave effect to what was, in any event, a moral obligation owed to the judgment creditor.” Restatement (Third) of Restitution and Unjust Enrichment §18 cmt. e (Am. Law Inst. 2011) (emphasis added). Instead, the Restatement ties an entitlement to restitution to the legal validity of the underlying debt or liability, explaining that, while “[a]n invalid or erroneous judgment that gives effect to a valid liability does not create unjust enrichment,” a “restitution claim based on legal compulsion stands on a different footing” when it is based on “money…paid to satisfy a claim that is valid in equity and good conscience yet legally unenforceable.” Id. (emphases added). Thus, when a debtor has been “compelled by law to pay a claim that is not legally enforceable…[t]he need to remedy this misapplication of legal process…constitutes an important reason for restitution that is independent of the individualized equities of the parties.” Id. Appellees’ immense default judgments against Cuba reflect the horror of those acts that Cuba is alleged to have committed against their family members between 1959 and 1976. In determining whether Appellees were “unjustly enriched” for equitable purposes by receiving the funds they have collected, however, we must weigh the legal validity of their underlying claims, not the relative moral standing of the parties. Here, as set forth in Section I.C, supra, Appellees articulate no sound or even plausible jurisdictional basis under section 1605A for their claims or for the judgments entered. This void suggests that the consequent turnover orders are not expressions of an underlying “valid liability” that some merely ancillary technical ground has made unrecoverable.30 Rather, Appellees have collected substantial funds pursuant to void turnover orders in a case where the District Court had no basis in law for exercising jurisdiction. We are compelled in these circumstances to rule that restitution is warranted. The unavoidability of this conclusion is underscored by our prior rulings. In Vera II, in which we dismissed BBVA’s attempt to directly appeal the District Court’s turnover orders, we held that we lacked appellate jurisdiction because the orders did not effect injunctive relief of the type that is immediately appealable, and because BBVA could not show that the orders “‘(1) might have a serious, perhaps irreparable consequence; and (2) can be effectually challenged only by immediate appeal.’” Vera II, 651 Fed. App’x at 26 (quoting Bridgeport Guardians, Inc. v. Delmonte, 537 F.3d 214, 220 (2d Cir. 2008)). The turnover orders did not work an irreparable harm on BBVA’s interests, we reasoned, because “the mere loss of funds pending final judgment can be remedied on appeal through recovery of the funds with interest.” Id. And, in May 2017, when the District Court denied BBVA a further stay and ordered that the funds deposited in the Court Registry be disbursed to Appellees, it expressly relied on this statement. See Vera v. Republic of Cuba, No. 12-CV-1596 (AKH), 2017 WL 4350568, at *2 (S.D.N.Y. May 25, 2017) (“As the Second Circuit held when denying BBVA’s appeal for lack of jurisdiction, BBVA has failed to show that the Turnover Order would ‘have a serious, irreparable consequence’ because ‘the mere loss of funds pending final judgment can be remedied on appeal through recovery of the funds with interest.’”). Indeed, with subject-matter jurisdiction at the very least an open question throughout this proceeding, the Villoldos, Hausler, and Vera all can fairly be said to have assumed the risk of sustaining an adverse ruling on appeal when they opposed BBVA’s stay motion and sought execution of the turnover orders before appellate review was complete. See PSM Holding Corp. v. Nat’l Farm Fin. Corp., 884 F.3d 812, 823 (9th Cir. 2018) (judgment creditor “assumed some amount of risk when it opted to execute on the judgment while an appeal was pending”); Strong v. Laubach, 443 F.3d 1297, 1300 (10th Cir. 2006) (same). In reaching our decision, we acknowledge the complexities surrounding BBVA’s possessory interest in the funds. On the one hand, we agree with Appellees that BBVA’s concern about confronting double liability is speculative at best. And, even if BBVA might be entitled to an equitable lien on the funds to the extent it has sustained costs related to its vigorous defense of the Cuban corporation’s assets, it has not yet presented any documentation of the attorney’s fees that it has incurred in this action, and its entitlement to recover them may, in any event, be subject to legitimate dispute. On the other hand, we note that, even if BBVA does not have a possessory interest in the funds, it may well have an interest in completing the transfer of the funds to the Cuban Import Export Corporation, now that the funds transfer is no longer blocked by the United States.31 We ultimately conclude, however, that the strength (or weakness) of BBVA’s interest in the funds does not provide an adequate basis for denying restitution to BBVA. When a party seeks restitution of funds collected from it pursuant to an invalid judgment, it is not ordinarily required to establish the nature of its possessory interest in the lost funds. Rather, the baseline rule in this Circuit is that “a party against whom an erroneous judgment or decree has been carried into effect is entitled, in the event of a reversal, to be restored by his adversary to that which he has lost thereby.” LiButti v. United States, 178 F.3d 114, 120 (2d Cir. 1999); see also In re Craig’s Stores of Texas, Inc., 402 F.3d 522, 525 (5th Cir. 2005) (“[W]hen the underlying litigation was dismissed for lack of jurisdiction, the disputed registry funds should have been disbursed back to the party that deposited them in the registry.”). Of course, we may decline to apply this rule if equitable considerations counsel otherwise. See LiButti, 178 F.3d at 120 (“[T]his rule is not without exceptions.”). But as discussed above, the equitable considerations at play in such a restitution analysis principally concern whether restitution is necessary to avoid unjustly enriching the party that benefited from the enforcement of an invalid judgment. For the reasons already stated, we conclude here that Appellees were unjustly enriched by enforcement of the void turnover orders, and that equity and good conscience require restoration of the status quo ante, particularly given (1) the absence of an underlying valid liability, and (2) Appellees’ decision to seek execution of the turnover orders, notwithstanding the substantial and apparent risks that the orders were vulnerable to reversal on appeal. Accordingly, we direct the District Court on remand to enter an order requiring restitution by Appellees of the funds that BBVA paid them under the void turnover orders. We have reviewed the parties’ additional arguments and conclude that they are unavailing. CONCLUSION The District Court lacked subject-matter jurisdiction over this enforcement proceeding under TRIA. The turnover orders that it issued in the enforcement proceeding were void ab initio. Accordingly, we REVERSE the judgment of the District Court, VACATE the turnover orders, and REMAND the cause to the District Court with instructions to (1) dismiss the amended Omnibus Petition and (2) issue an order directing Appellees to return to BBVA the funds that BBVA paid them under the void turnover orders. JOSÉ A. CABRANES, C.J.: I join the judgment of the Court.