The resort refillable mugs can be refilled at the Counter Service food courts at that resort. Shutters is the TS restaurant at CBR, so the mugs would not be needed or filled there. Shutters is in the same building as the food court, so if you want to bring our mug to fill before heading back to your room after dinner I think it would be fine to keep them in a bag and store them like your purse until you leave the restaurant.