Problem: A small percentage of guests bringing back old refillable mugs and using them for various reasons, including "I don't want to pay $10/$12/$15/$18 for a new mug".
Solution: Lower the price on the refillable mugs to encourage more guests to buy one for each family member on each trip. Volume of mugs bought would/should make up for a lower price, not to mention repeat business, since guests would likely not be averse to purchasing a new mug on each trip because the cost would be lower/manageable.
DIS Solution: Raise prices. Spend hundreds of thousands, if not millions, instituting the RapidFill program. "That'll show'em!"