A panel of federal appeals judges were doubtful Tuesday of what additional information could be gleaned about Hillary Clinton's emails if the former secretary of state were to sit for a deposition in a public records case.

Judges Thomas Griffith, Cornelia Pillard and Robert Wilkins of the U.S. Court of Appeals for the D.C. Circuit heard the arguments after U.S. District Judge Royce Lamberth of the District of Columbia ruled last year that Clinton could be deposed in a Judicial Watch Freedom of Information Act lawsuit for records relating to the 2012 Benghazi terrorist attack. Clinton's lawyers at Williams & Connolly, led by David Kendall, intervened and petitioned the circuit to vacate Lamberth's order.

On Tuesday, Judicial Watch attorney Ramona Cotca told the court that the group had remaining questions over the handling of the emails. "The issue is identifying all sources where Clinton emails reside, and for the State Department to do an adequate search," she said.

"The State Department now has every incentive to get to the bottom of this if you have any questions, if that's the case," Pillard replied. "This is no longer Secretary Clinton's State Department, this is the Trump State Department."

"It doesn't matter who the administration is, but the issue is," Cotca began before Pillard cut her off. "It does in the sense of whether you think—from what I gather you're saying is that there's some kind of cover-up," the judge said. "And so I'm just trying to understand why you think this is relevant under FOIA, the claim you brought."

Cotca denied the group believes there was a cover-up over the handling of Clinton's emails. Rather, she argued, emails recently handed over to the State Department by the FBI raised fresh questions over whether all possibly relevant emails were searched.

Pillard in particular was skeptical of that claim, noting the State Department later found it had already possessed those same emails and found they were not relevant to Judicial Watch's records request.

The judges also questioned how the deposition fits into the public records law, which they and Clinton's legal team said only requires federal officials to do a fair and reasonable search for responsive documents.

"If the question is whether there's been an adequate search, what difference does it make what the intent was or reasons for using a private server, or Hillary Clinton's or anyone else's understanding of State's record searching obligations?" Wilkins asked. "How does that prove this search, which was conducted since Secretary Clinton left office, was adequate?"

And the judges also pressed a question they had presented to the parties ahead of the case, on whether it was moot due to another circuit decision over State Department records. Kendall said the case was moot, but Cotca and Justice Department attorney Mark Freeman, who also argued Tuesday, said it was not.

Kendall told the court the deposition could be harassing, saying footage of a video deposition could be used by Judicial Watch for political or fundraising needs. But Griffith questioned why the deposition would have to be filed in the first place, and asked if the footage could be sealed. Griffith also said that, if Kendall is right about his client not having much more information, "the line of questioning won't last very long."

"The purpose of this discovery, even if it was sealed, is simply harassment," Kendall said. "It's not authorized by the law, or the court, or other precedent."

Freeman, the DOJ attorney, said the federal government is not taking a position in the case.  "The State Department's approach for all of these cases, from the beginning, has been to just get through them," he said of the Clinton FOIA litigation.

And he said DOJ was not backing Clinton's petition as the government itself had not sought the relief. "We chose in the interest of the executive branch, balancing pros and cons, not to do so here," Freeman said.