Gathered with her colleagues for one of the last times in the offices of the Ed Sullivan Theater, Jude Brennan, an executive producer at CBS’s “Late Show With David Letterman,” was reflecting on how she started working for the host some 35 years ago.

Ms. Brennan, who has collaborated with Mr. Letterman on his short-lived NBC morning show, on NBC’s “Late Night” and now on “Late Show,” explained that this kind of devotion was its own special calling.

“It’s not just a job,” she said a few days ago. “It’s something else.”

Here, Steve Young, a writer for Mr. Letterman since 1990, chimed in. “It’s community service,” he said, to knowing laughter from his co-workers.

On Wednesday, when Mr. Letterman brings down the curtain on his final “Late Show” broadcast, it is not just his own 33-year history in late-night television that is coming to a conclusion.