Removing patches?

I'm sure this has been discussed before, but...

Anyway, just finished rewatching all of SG-1 and now I'm on season 1 of SG:A.

From their very first off-world trip everyone from Atlantis removed their patches on Teyla's planet. Everyone says so they can hide the fact they're from Atlantis, however at the time they didn't know there was any threat until after Teyla told them of the Wraith. Besides, they seem to tell everyone they're from Atlantis anyway.

Removing the flag patches doesn't make any sense. It's not like anyone in the Pegasus galaxy is going to see a patch with some colored stripes, stars, or a red leaf and know what it means.

SG teams from Earth however, had no problem wearing the point of origin symbol for Earth on their jackets.