Mr. Wheeler faces at least one formal complaint, by the nonpartisan government watchdog group Public Citizen, alleging that he “appears to be working on the same specific issue areas he had lobbied on within the last two years.” That is a potential violation of President Trump’s ethics rules limiting the influence of former lobbyists on the government, the group asserts.

Mr. Wheeler’s critics point in particular to his lobbying disclosure filings, which describe his lobbying activities only in general terms that they say fail to adequately reveal what he actually worked on the past eight years. “If I had it to do over again, I would have been more specific,” Mr. Wheeler said. “But when I started lobbying I didn’t really anticipate ever going back into the government.”

However, by the time the 2016 election came around, Mr. Wheeler said he began shedding his E.P.A.-related lobbying, anticipating that he might be called on to join the Trump administration. “I knew it was a possibility, so after the election I stopped lobbying any new E.P.A. issues,” Mr. Wheeler said.

One of Mr. Trump’s earliest executive orders, aimed at fulfilling his promise to “drain the swamp” in Washington, permitted former lobbyists like Mr. Wheeler to join the administration as long as they did not meet one-on-one with former clients or work on any specific matters they had handled in private practice in the previous two years.

Mr. Wheeler, along with Justina Fugh, the E.P.A.’s senior counsel for ethics, said he had not sought or received any ethics waivers. Such special dispensations have been granted to dozens of people throughout the administration to bypass Mr. Trump’s executive order and allow them to work on the matters on which they lobbied.

“I think that’s an ethical cloud if you have a waiver. I personally didn’t want to do that,” Mr. Wheeler said. “Because I was a lobbyist, and that was made a big deal during my confirmation process, I just wanted to be on safe ground there.”