What is it?
It was a joke for the DS9 episode Trials And Tribble-ations
. And nothing more.
It wasn't presented in the episode as a joke in the Universe itself. Rather, it was presented as a real agency that actually exists in the Trek Universe.
Well duh, really? I know that much. What I tried to say is that it was merely meant as a joke by the writers. There didn't really went much thought into that beyond "let's invent this angency as a plot point for our story and get a few laughs out of those two agents". (Which worked magnificently, if you ask me.)
In my opinion it were Voyager
and later Enterprise
(not Deep Space Nine
) who, with their invention of the Temporal Integrity Commission, took the real life implications of time travel way too seriously. If time travel really was possible, I very much doubt there would be any such agency.