I travelled to India on AP in June this year. Port of entry was Detroit. Absolutely no problems. They simply stamped both copies of the original AP, kept one copy for their records, gave me the other copy and let me go. All you need to show them is a valid passport and the 2 original copies of the AP that TSC mailed you. For your own peace of mind you might also want to carry a copy of your 485 receipt notice and an employment letter.
Hope this helps. Good luck.