They do? I always thought they kept them on.

Disregard my last comment, I have a theory on this and I believe it's related to the faction within the Pegasus Galaxy called the Geni, these people have spies everywhere throughout the Galaxy, and their spies know the insignia of the atlantean team, and I believe the team do that so that nobody knows who they are and hopefully they won't tell them apart from the Geni.

Just a theory.

Maybe, they are off duty after the missions.

It’s common practice in the United States military to remove unit patches when going on mission.