Your KTTW card charges are applied to your room, not your credit card. It accumulates until you pay it off / check out.
Your KTTW card balance can be paid by any method before you check out. However, it has been my experience that resort staff do not allow you to pre-pay your charge priveliges. (I was trying to increase the credit limit so I could eat more fancy food without stopping to pay my balances every 2-3 days.)
In summary, the KTTW charge priveledges are essentially guaranteed by your credit card on file for your room. But you can pay off these balances anytime by any method, including cash.