Another person commented below about the Carter thing. She wondered if the writers retconned it later. Apparently there were no female pilots during the Gulf War. Either that, or she wasn't there long enough to qualify as a tour. You have to be overseas 300 days in 18 months for a short tour.

It's possible that it isn't a silver star. It could be a Global War on Terrorism Badge, though I can't see the yellow in it.