They're spies in the same way James Bond is a spy. I.E. they are actually troubleshooters.
Jerry, much like M, only calls on them when he knows that there is something going on, what the general plan is, where to send them and who the probable bad guy is. The real spying has already been done.
He then sends them in to verify the information, reveal any real bad guys behind the original and kick ass. Jerry sends them to capture people, much like m sends Bond to kill people.
Their clothes IMO have the same purpose as Bond announcing his name to everybody he meets and never using fake names. It's an advertisment. It's intimidation. It's saying WHOOP/England has found your scheme, now you're fucked. You know someone is coming for you, you're getting captured/dead, and everyone in the spy game is going to know we did it, and that we can do it to them.