What would you do in this case?

Yes, they probably used an air impact wrench and cross threaded the lug nut on. If its a major chain don't mess around with the people at the shop, call headquarters. If its a privately owned place it could be a bit more complicated that just a quick call to HQ. I would recommend being a bit demanding about this. If you need a new one demand the place foots the bill. Faulty work is faulty work, period.