Square badge with the USAs on it. Was introduced in the early 80's (briefly dropped in favor of the "Drop G" stopsign badge) and then brought back and used all through the rest of the 80's, thru the 90's, and on into around 2005 or so (I think). At around that point, before they went back to a revised stopsign design (and ultimately back to the round badge) they changed it so it didn't have the USA's on it, replacing that with "since 1883" on each side.
There was a pewter colored version used on the USA Maple series and also the earlier Broadkaster series. Another silver version, blank in the area where the USAs were, was used on imported drums.
So this particular badge had a long run and therefore isn't particularly helpful in dating Gretsch drums. A drum with that badge could be from anytime between 1980 and (roughly) 2005.
As I mentioned above, the muffler would lead me to think this was on the older end of the spectrum but it was possible to order a drum with a muffler installed all through that time frame, although it probably didn't happen a lot.
What is the color and information on the paper tag inside (if there is one)?