Cut the apple slices in the pie filling into smaller pieces. Add cold milk to a mixing bowl and sprinkle pudding mix over the milk. Mix with a handheld mixer on low speed for 2–2.5 minutes until it thickens. Lay a single layer of graham crackers in the bottom of a 9×13 baking dish, breaking them as needed. Spoon ½ of the cut apple pie filling evenly over the graham cracker layer. Spoon ½ of the pudding over the apple pie filling and smooth it out. Repeat the layers of graham crackers, apple filling, and pudding. Finish with a final layer of graham crackers on top. Spread caramel topping over the top layer of graham crackers and chill in the refrigerator for 4 hours. Cut into 3 slices x 5 slices before serving and store leftovers in the refrigerator for up to 3 days.