Did they? I thought "The Jem'Hadar"'s model work was done before AGT, and the few later Galaxy-class appearances were either stock footage or (once you get into the Dominion War) CGI.
It was used one last time in Way of the Warrior as the USS Venture. It retained the attachments from the AGT modification on the tops of the warp nacelles.
I guess they didn't cover up all the scars after all. You can see some smudging on the saucer around where the registry should be.
I think the smudge has more to do with hiding the registry since the ship isn't supposed to be the Enterprise.