Yes you can return items to Advance Auto Parts without the receipt or proof of purchase however you will not receive cash back or money back to your credit or debit card for returns of items or parts to Advance Auto Parts without the receipt.
Instead if you return an item or parts to Advance Auto Parts without proof of purchase or a receipt they will issue you a store Merchandise Purchase card to be used at Advance Auto Parts stores.
So you can get something else after returning the merchandise to Advance Auto Parts without the receipt.
The parts or items you return to Advance Auto Parts must be New and in original condition and packaging, unopened and uninstalled, including all original materials supplied with the part or items for the return to happen.