Mr. Perlmutter is the former chief executive of Marvel Entertainment, Mr. Sherman is a lawyer and Dr. Moskowitz is a doctor. The three do not possess special expertise in veterans health care issues, but were reported to be influential over Trump administration policy, including its plans to push the department’s health care system toward private providers. The three are frequently at Mar-a-Lago, Mr. Trump’s private club in Palm Beach, Fla.

According to a report last year by the nonprofit investigative news organization ProPublica, the three pressured Mr. Trump’s first veterans secretary, David J. Shulkin, then peppered him with demands before ultimately working with personnel in the department to oust him. The group also pushed — in most cases, unsuccessfully — for certain vendors to manage health care records, and had a direct line to the president.

“I think most Americans would agree that wealthy private citizens should not be having back-channel influence” on veterans services, Mr. Takano said in an interview Friday. He said that he could use his subpoena power as a “last resort” if the requested documents were not relinquished. “This doesn’t have to be a drama,” he said. “It is a legitimate request.”

The three men released a joint statement in response to the committee action.

“We were asked by the president and, repeatedly, by the former secretary and his senior staff to assist the V.A. in enhancing the level of service it provides to our veterans,” the statement said. “Our primary focus was to introduce the V.A. to experts in various areas where V.A. staff asked for our help. We do not regret trying to do our small part, and even given the unjust and unrelenting criticism we have faced, each of us would step in to help our veterans again.”

A spokesman for the new veterans secretary said he rebuffed outside pressure of the kind ascribed to the three men.