For months, John Jay Ray III, the corporate turnaround expert who was appointed to oversee the bankruptcy of the FTX crypto exchange, has attacked the company’s founder, Sam Bankman-Fried, accusing him of “old-fashioned embezzlement.”

Now, Mr. Ray has a new target: Mr. Bankman-Fried’s parents.

On Monday, FTX filed a lawsuit in federal court in Delaware accusing Joe Bankman and Barbara Fried, longtime Stanford law professors, of using their “access and influence within the FTX enterprise to enrich themselves.” The lawsuit seeks to claw back millions of dollars the couple received from their son.

In the complaint, FTX’s lawyers said that Mr. Bankman and Ms. Fried got a $10 million cash gift from Mr. Bankman-Fried, as well as a $16.4 million home in the Bahamas, where FTX was based, that was purchased by the exchange. The suit also claims that Mr. Bankman helped cover up complaints by a former lawyer for his son’s business, and that Ms. Fried coached Mr. Bankman-Fried and another FTX executive to evade disclosure requirements for political donations.

The couple “either knew — or ignored bright red flags revealing — that their son, Bankman-Fried, and other FTX Insiders were orchestrating a vast fraudulent scheme,” the lawsuit said.

A spokeswoman for Mr. Bankman and Ms. Fried did not immediately respond to a request for comment.

FTX filed for bankruptcy protection in November, after a run on deposits exposed an $8 billion hole in the exchange’s accounts. The next month, federal prosecutors in Manhattan charged Mr. Bankman-Fried with orchestrating a scheme to use customer deposits to finance billions of dollars in venture capital investments, political donations and luxury real estate purchases. He has pleaded not guilty, and is scheduled to go on trial on Oct. 3

FTX’s collapse fueled scrutiny of Mr. Bankman and Ms. Fried. A decorated tax professor, Mr. Bankman was an FTX employee who was heavily involved in the company’s philanthropic efforts, while Ms. Fried, also a respected scholar, ran a political-donor network that her son helped finance.

According to the lawsuit, Mr. Bankman helped arrange hundreds of millions of dollars in loans to top employees and was listed on an internal document as a member of the firm’s management team. In messages cited in the lawsuit, Mr. Bankman complained that he was receiving a salary of only $200,000 a year, as opposed to the $1 million he thought he would get.

“Gee, Sam I don’t know what to say here,” he wrote in an email cited in the suit. “This is the first [I] have heard of the 200K a year salary!”

Soon after, Mr. Bankman-Fried sent him the $10 million gift, the lawsuit said. Mr. Bankman also flew on private jets and expensed $1,200 per night hotel stays to FTX, according to the lawsuit, and he made a cameo appearance alongside the comedian Larry David in an FTX commercial during the 2022 Super Bowl.

Mr. Bankman pushed for his role in the commercial, the lawsuit said, quoting him as saying that he wasn’t obsessed with celebrities and didn’t “really care about meeting, say, Tom Brady. But Larry David….”

The lawsuit also claims that Mr. Bankman helped cover up allegations by a former FTX lawyer that some of Mr. Bankman-Fried’s businesses had engaged in money laundering and price manipulation. Rather than look into those claims, the lawsuit said, Mr. Bankman suggested investigating the lawyer.

Ms. Fried never worked for FTX, but she was also intimately involved in her son’s work, the lawsuit said. According to the complaint, she advised him on political donations, encouraging him and other executives to make “straw donations” that concealed that the money was coming from FTX, a strategy designed to “avoid (if not violate) federal campaign finance disclosure rules.”

In an August 2022 email to Mr. Bankman-Fried, cited in the suit, she brought up another donor who would “only give in a non-disclosed form” and said she “would strongly urge you to do the same — or substitute someone else’s name.”

Federal prosecutors have accused Mr. Bankman-Fried of orchestrating a straw donation scheme, and two of his top advisers, Nishad Singh and Ryan Salame, have pleaded guilty to participating in it.

Mr. Bankman and Ms. Fried were frequent visitors to the Bahamas, staying at a 30,000-square-foot property with ocean views. Since FTX’s collapse, the couple has claimed they “never believed” they owned the house. But according to the suit, a subsidiary of FTX paid for the home; Mr. Bankman emailed a top FTX executive in May 2022, inviting him and others over to “celebrate the house you helped us buy/move into,” the complaint said. He and Ms. Fried were granted permanent residency in the Bahamas last October, the suit said, with FTX covering $30,000 in fees associated with the applications.

Mr. Bankman also asked FTX employees if the company that provided landscaping services for the house could bill FTX directly, according to the lawsuit. And one month after the purchase was closed, the complaint said, Ms. Fried instructed FTX employees to place online orders for a sofa, at least eight vases and a Persian hand-knotted rug costing more than $2,500.