On the uniforms of both the SG teams and the SGA teams patches are featured. On Atlantis the patches are the Mission Patch and the flag of the country that the team member hails from.
Why are those patches removed, when the teams go through the Gate? Just to make sure, that people the teams meet are unaware of the origins of the team seems to be not a valid point, as by first contact no one would recognise either the flag or the mission patches...