Store any leftover Oreo dirt cups in the refrigerator for up to 3 days. Keep the cups tightly covered with plastic wrap to prevent the cream from absorbing refrigerator odors. You can freeze the un-garnished cups for up to 2 weeks if you seal them inside an airtight container. The cookies will lose some crispness the longer they sit in the fridge. Do not try to reheat this dessert because the whipped topping and pudding will melt into a sweet liquid soup. If the top cookie layer looks dry after storage you can sprinkle a tablespoon of fresh crumbs over the surface. Check for spoilage by looking for separation where liquid pools at the bottom of the plastic cup.