The combined result — eliminating the ban on hiring former lobbyists and keeping secret any waivers granted to new hires — means the public has no way of knowing if Mr. Trump’s staff members are complying with the rules. Terminating the release of the White House visitor logs, which were public during the Obama administration, has made evaluating compliance even harder, as it is now not known which private-sector players are meeting with White House aides.

For example, Michael Catanzaro, who until recently worked as a lobbyist for companies like Devon Energy and for the American Fuel and Petrochemical Manufacturers association, is now in charge of White House environmental policy, an issue related to the topics he handled as a lobbyist. He may or may not have been granted a waiver by the White House. A White House spokeswoman declined to say.

The White House, in a written statement, said officials were reviewing Mr. Shaub’s request and had not decided how to respond.

“However, in the meantime we would like to reiterate our position that the White House and the White House Ethics Office are fully compliant with ethical obligations set forth in the standards of conduct,” the statement said. “Anyone that claims otherwise is purposefully mischaracterizing the White House’s position.”

Mr. Shaub has tried to at least force the White House to make any waivers public. He is doing so by using his power to issue a “data call” for copies of all waivers issued in the last year. That would include the final months of the Obama administration and the first four months of the Trump administration.

He has quietly escalated his battle with the White House. A second letter he sent late last week to the top senators on the Homeland Security and Governmental Affairs Committee also made clear that the ethics office intends to make a similar request early next year that will cover all such waivers granted in 2017.

Mr. Shaub made headlines when he authorized his staff to publish a series of Twitter posts in December related to how Mr. Trump would separate himself from his family business operations. Then, in January, in an unusual public statement, Mr. Shaub called Mr. Trump’s steps “wholly inadequate,” even though Mr. Shaub did not have the power to order Mr. Trump to take additional steps.