WASHINGTON — Less than two years ago, Scott Garrett, then a Republican congressman from New Jersey, took to the floor of the House of Representatives and laced into his colleagues for resurrecting an institution that “embodies the corruption of the free enterprise system.”

The institution he derided was the Export-Import Bank. He could soon be running it.

In April, President Trump tapped Mr. Garrett, who lost his seat to a Democrat last November, to lead the bank, a federal agency that provides loan guarantees to American companies selling to foreign customers. For years it has been a political punching bag for conservatives who have called it a tool of corporate cronyism and a meddler in free markets. Mr. Trump frequently assailed the bank while on the campaign trail.

Mr. Trump reversed himself last month, though, and decided to keep the bank alive, coming to the conclusion that it helps small businesses and allows American exporters to compete more effectively around the world.

But the choice of Mr. Garrett was widely viewed as curious. As one of the bank’s most ardent conservative Republican critics, he had argued forcefully that it should be shuttered. As a critic of the organization that he has been asked to lead, Mr. Garrett fits the mold of the deconstructionists who Mr. Trump found appealing in forming his cabinet, like Rick Perry at the Department of Energy and Scott Pruitt at the Environmental Protection Agency.