They should be able to look up for purchases through your membership account or credit card. So they should be able to help you even if you don't have your receipt. A few times I didn't have my receipt and that is how they looked it up for me so I could exchange my item.
I do believe you need a receipt but suggest you call Costco to find out. Good luck.
No. Costco keeps good records, so it's not a problem.
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