A website is tricking people into thinking they're dealing with Delta Air Lines when arranging for their pets to fly on jets, the Atlanta-based company maintains in a new federal lawsuit.

The site—DeltaPetTransit.com—is designed to look like a Delta site and uses the airline's logos and pictures of its planes, Delta said in the lawsuit, filed Thursday in U.S. District Court in Georgia. But the site isn't affiliated with the airline and has no right to use its trademarks the complaint says.

The website solicits pet-shipment payments while posing as Delta, but offers no services, Delta maintains.