The emails from Trent Morse, the deputy director of the White House’s personnel office, arrived in the inboxes of three Biden-appointed commissioners at the National Capital Planning Commission on July 9. They were terse and came without warning.

“On behalf of President Donald J. Trump, I am writing to inform you that your position as commissioner of the National Capital Planning Commission is terminated, effective immediately,” Mr. Morse wrote. “Thank you for your service.”

The little-known board, which has the relatively mundane task of reviewing the impact of development projects on the capital’s urban landscape, was barely on President Trump’s radar during his first term. But the panel, which does not oversee projects or consider their cost, has since become pivotal in the administration’s campaign to discredit Jerome H. Powell, the chairman of the Federal Reserve, whose departure the president is trying to accelerate.

Mr. Trump has become increasingly angry with Mr. Powell for being too slow to cut interest rates, and his advisers have been weighing whether to try firing him, a legally precarious escalation. In recent weeks, White House officials have focused their attention on the cost of renovating the central bank’s headquarters in Washington, suggesting that Mr. Powell’s handling of the $2.5 billion makeover could be grounds for sacking him before his term ends next year.

The controversy over the cost of the renovations has thrust the National Capital Planning Commission, a 12-person panel that was created by Congress in 1924, into a rare political spotlight. The White House’s sudden interest in the commission has turned it into a cudgel that could potentially alter the makeup of the Fed at an important moment for the U.S. economy, which is facing a new bout of inflation from Mr. Trump’s tariffs. The president has made clear he wants to install a chair who will cut rates despite concerns that import taxes could lead to higher prices, a position that could result in even more inflation if low borrowing costs overheat the economy.

Mr. Morse’s letters were sent to Teri Hawks Goodmann, Bryan C. Green and Elizabeth M. Hewlett. The former commissioners, who have backgrounds in urban planning and architecture and serve on the commission on a part-time basis, were appointed to six-year terms under the Biden administration.

Ms. Goodmann, who was the chairwoman of the commission, was preparing to fly to Washington from Iowa for a meeting when she received the notice that she was terminated. “The current administration had a different idea about how they saw the work of the National Capital Planning Commission,” she said.

Under the National Capital Planning Act of 1952, the commission is responsible for evaluating federal development projects in the Washington area to make sure they do not harm the government’s interests or functions.

Ms. Goodmann said she was not on the commission in 2019, when the renovation to the Fed’s headquarters was first being proposed. She said, however, that the commission did not assess matters of cost when evaluating how a project would affect the capital region.

“I am aware of how this is being interpreted,” Ms. Goodman added.

She was replaced as chair of the commission by William O. Scharf, the White House staff secretary who served as Mr. Trump’s personal lawyer. The president’s other appointees were James Blair, his deputy chief of staff, and Stuart Levenbach, an energy official in the Office of Management and Budget.

Mr. Trump’s budget director, Russell T. Vought, discussed the Fed renovations at the White House on Thursday, explaining that the president had “substantial concerns” about Mr. Powell’s performance and claiming that he had “horribly mismanaged” the building project. Mr. Vought added that he wanted to personally review the project.

“I want to see it, I want to walk around the building, with the other members of the commission,” Mr. Vought said, suggesting that Mr. Powell had lied to Congress about the construction costs in recent testimony. “It’s either misleading the Congress, or it needs to go back to the planning commission.”

The Fed’s renovations were not on the original agenda for the planning commission meeting last Thursday. After two hours of discussion about other projects, Mr. Blair raised it as a matter of concern.

“Some have started to refer to this as the Taj Mahal near the National Mall,” Mr. Blair said, arguing that the renovation was not in line with the “modest and restrained” design principles that were proposed in 2019.

Mr. Blair has also kept up his criticism of Mr. Powell on social media, posting a meme of the central bank chairman dressed as Marie Antoinette that read, “Let them eat basis points.”

The Fed is self-funded, meaning its operations and the renovations are covered by the proceeds garnered from bank fees and investments of government securities rather than money allocated by Congress. Mr. Blair argued that the government still had a responsibility to ensure that the central bank was spending money responsibly and suggested that the Fed had strayed from its original plans to pursue a more extravagant building.

“There is at least some responsibility to protect the federal government’s interests,” he said. “I think it is squarely in the federal government’s interest to ensure that dollars that do ultimately originate from the taxpayer, whether through appropriations or in this case through the exercising of monetary policy, are well spent. We should not be made fools of by those who came ahead of us.”

Mr. Powell defended the project in a letter to Mr. Vought on Thursday that said the planning commission did not officially have oversight over the Fed’s renovation. The project was scaled back from the original proposals that were approved, he noted.

The Trump administration believes that because the Fed has not been profitable enough to send money back to the Treasury Department, the White House has a right to scrutinize its spending practices. Mr. Blair requested a full review of the Fed project, including any changes to the original plan, and a visit to the building. The Fed has not said if it will allow such a tour.

The Fed’s project, which kicked off in 2021, is estimated to be $700 million over budget. The bulk of the renovation entails expanding and modernizing the Marriner S. Eccles Building, which was built in 1935, and the 1951 Constitution Avenue Building, which was built in 1932.

But the initial plans for the complex, which was designed by the French architects Paul Philippe Cret and Jules Henri de Sibour, and other changes to the classical buildings included additions, a new parking garage, atriums and skylights. The Fed has said that plans for water features and other changes were scaled back as the costs of the project grew.

The cost overruns stemmed in part from the very thing the central bank has been trying to stamp out for the past three years: inflation. In an explanation of costs of the project on its website, the Fed blamed “differences over time between original estimates and actual costs of materials, equipment and labor.”

The planning commission approves projects in conjunction with the U.S. Commission of Fine Arts, which focuses on the architectural attributes of construction and renovations. Some of the additional costs related to the Fed project stemmed from requests by members of the panel who were appointed during the first Trump administration and pushed in 2020 for the use of more traditional materials such as marble over more the modern aesthetic of glass and steel.

“It’s kind of ironical that Trump is railing against this thing, but he appointed people who did delay the project at the time by prolonging reviews for things that probably made it more costly,” said Alex Krieger, an emeritus professor at the Harvard Graduate School of Design, who was on the Commission of Fine Arts in 2019.

Mr. Krieger, who was appointed to that role during the Obama administration, said the changes ultimately were not the main drivers of the additional expense of the project.

“In any kind of historic preservation project, the initial estimates of what it would cost to fully renovate it is rarely the cost of what it winds up being,” he said.

Duncan G. Stroik, an architecture professor at the University of Notre Dame who was appointed by Mr. Trump to be on the fine arts commission, said that the cost of the project was not considered at the time, but that $2.5 billion was an astronomical price for a building that houses an institution dedicated to sound economic management.

“I like nice buildings, and I like spending money on buildings, and I think that’s crazy,” Mr. Stroik said.

It remains unclear whether Mr. Trump will use the renovation controversy as a pretext to fire Mr. Powell.

At the White House briefing on Thursday, Karoline Leavitt, the press secretary, said “it's a hypothetical question, we’ll see where it goes” when asked about firing Mr. Powell after a review of the renovation.

The planning commission’s meetings are usually mundane events focused on land use issues rather than contentious political matters. But when it convenes in September, the proceedings that will be led by Mr. Trump’s new appointees will be closely watched as the world awaits Mr. Powell’s fate.

“In my time, it’s been absolutely apolitical,” said Mr. Green, an architectural historian at Virginia Tech, who was removed from the commission last week. “I don’t remember any discussion we ever had that was charged by politics. We were never given direction.”