The GEM is the Generic Electronic Module... That's not a cheap part, but any do-it-yourselfer can change it in about 20 minutes...
Sounds like they didn't do a proper diagnostic and preferred to just throw parts at it instead. Before I ever authorize a repair, I want to know what's broke, and not why they think it's broke, but what testing they performed to know it's broke.
In this case, it should have started with retrieving the DTC, which should have been a P1260 if the PATS system was activated. Then, it should have gone on to check the service manual which outlines the diagnostics for the PATS system... If the transceiver was bad, the system would have thrown a B2103 or B1232 DTC (antenna not connected defective transceiver) indicating as such. They should not have replaced it unless they had ascertained through a PROPER diagnostic that it was bad in the first place.
I despise shops that operate like that. (i.e. parts changers) If they'd take the time to do it right, we wouldn't have these problems...
-Joe