The day before you check out there will be a ME envelope delivered to your room with instructions, pick up time, etc. There is a phone # to call to make any baggage payments with your credit card. You'll get a confirmation number to take to RAC, though when I have done this RAC was able to see in their computer that the fees were paid and didn't ask me for the confo number.
Do NOT call the airline or go online to the airline website to make this payment, as that will lock your airline record in RAC's system and they won't be able to check you in at all.