So-called certificates of divestiture are offered to incoming federal employees as a way to make it easier for the wealthy to take government jobs without major tax consequences. But Mr. Shaub has questioned if Mr. Scaramucci is entitled to such a benefit because he had entered into a deal to sell his stake in SkyBridge before he was hired for the White House communications job.

Mr. Apol said he had not yet decided if Mr. Scaramucci should get the tax benefit.

“The test whether we issue a CD is whether or not it meets the requirements in the law,” Mr. Apol said, referring to the certificate of divestiture. “If it does, we will; if it doesn’t, we won’t.”

In the past seven months, Mr. Apol has played a central role in making major ethics decisions related to the Trump administration, including reviewing the financial disclosure report and issuing certificates of divestiture for Jared Kushner, the president’s son-in-law, and for other senior appointees.

Already, according to staff members at the Office of Government Ethics, Mr. Apol has advocated consulting with the White House before he issues certain policies — like one establishing rules related to legal defense funds that some Trump administration officials are setting up. He also wants to check with the White House before the office sends letters to members of Congress who have raised questions about White House ethics matters.

“Moves like this jeopardize O.G.E.’s independence,” Mr. Shaub said.

Lindsay Walters, a White House spokeswoman, said that Mr. Apol, who is serving in an acting capacity, is a positive change compared with Mr. Shaub, who often sparred with Mr. Trump.

“The White House welcomes a return to a traditional working relationship with the Office of Government Ethics in which both entities share a common goal of ensuring public confidence that the executive branch is adhering to the highest possible ethical standards as opposed to an approach whereby individuals manufacture false conflicts for purposes of self-promotion,” she said in a statement.

Other former agency employees said they wondered if at times Mr. Apol had gone too far in questioning agency standards.