You pretty much answered your question in the subject line. I had a 2001 GT that the synchronizer went out in third gear and the car was fixed under warranty. If your lucky you can get your's fixed under warranty as well.
synchronizer can loast for looong time if you don't abuse it. Meaning you match rev as close as you can to optimal RPM, and stuff. And if its making little grind, i wouldn't worry about it
As far as replacing worn synchro goes, it might be cheaper to look for used trans with good synchro. if you look right place, u can locate one for about $300~$400, and thats alot cheaper then to remove trans, open up trans, disassemble gear sets, make sure everything is with spec using fine instruments, replace synchoronizer ring, and re-assemble everything, and sitck it back on the car.
take trans off of car is really not that hard. few hours at most even for novice mechanic(aslong as you can take starter out).
my .02