The mysterious case of the dead giant rabbit continues to haunt United Airlines.

The owners of Simon, a 3-foot-long Continental Giant rabbit found dead after a transatlantic United flight, want compensation from the airline and an investigation into its policies for transporting animals.

Lawyers for the group of Iowa residents who bought Simon have sent a letter to United (UAL) threatening legal action if it doesn't respond within a week.

The death of the giant rabbit is just one of the PR nightmares United has run into in recent weeks. News of it emerged at a time when the airline was already reeling from the huge backlash over one of its passengers being violently dragged off a flight.

Three men pooled their resources to buy Simon for $2,330 from a British breeder with plans to make him a star attraction at the Iowa State Fair, according to their lawyer Guy Cook. They expected 10-month-old Simon would eventually inherit the crown of world's largest rabbit from his father, Darius.

In the letter to United, Cook accused the airline of a "failure to provide Simon the appropriate measure of care he deserved, which resulted in Simon's death."

United said in a statement Monday that it has received the letter and is reviewing it. "Our United team takes its responsibilities in transporting pets seriously, and is saddened by Simon's death," it said.

Related: A 3-foot-long giant rabbit is found dead after United flight

The rabbit's previous owner in the U.K. said that United had been in regular contact and the matter had been resolved to her satisfaction.

But Cook said that United hasn't done enough.

"My clients have suffered damages and United has taken no action to rectify this matter with my clients," he said.

Related: The new age of airline rage: Why everyone on board is on edge

What caused Simon's death after a flight from London to Chicago in April remains unclear.

United said he arrived at Chicago O'Hare airport "in apparent good condition" and was seen moving about in his crate about 35 minutes later. But shortly after that, a worker "noticed Simon was motionless and that he had passed away."

The problem now, according to Cook, is that United cremated Simon's remains without permission from his breeder or owners. United "cannot prove they acted responsibly, as they destroyed the proof," he said.

The letter to United demands that it hand over all records of the airline's investigation into the death, including any CCTV footage. The owners are also seeking compensation, including for "the economic loss of Simon's future attraction as the 'World's Largest Rabbit.'"

-- Samira Said contributed reporting.