When President Trump signed an order imbuing the so-called Department of Government Efficiency with even more power over the federal work force, Elon Musk was there, championing the work as an exercise in transparency.

“All of our actions are maximally transparent,” Mr. Musk said last week, standing in the Oval Office. “In fact, I don’t think there’s been — I don’t know of a case where an organization has been more transparent than the DOGE organization.”

But in case after case, federal judges have begged to differ.

The work of Mr. Musk, who Mr. Trump has said is the leader of the operation tasked with making “large scale” reductions across every department, has been largely shrouded in secrecy. Team members have spent weeks burrowing into multiple federal agencies, demanding access to data for undisclosed purposes.

Anxious career employees have received little direct information, leaving them reliant on office rumors and news reports for updates. The identities of the members of Mr. Musk’s team, too, have been closely held.

Court filings in the torrent of lawsuits challenging the incursions have offered a crucial, though limited, window. As some of the only firsthand accounts of what Mr. Musk’s associates are doing across a number of departments, they paint a picture of a tightly managed process in which small groups of government employees have swept in and out of agencies, grabbing up data in apparent pursuit of larger political projects.

The filings have also offered revelations about what information security and ethics trainings those employees have undergone. But many questions remain, frustrating the judges trying the cases.