Is using cardboard to repair headphones ok?

How about a make and model number so we can see what you're referencing? I hope you thanked your mother for being so thoughtful. I hate being given tee shirts from places I didn't get to go to. Return the favor after you get them fixed by loaning them back to your mom on her next flight. That may have been what brought brought them to mind when she didn't have a pair.

Oh, BTW, usually when I come back from a trip abroad, I'm out of cash and have to use a credit card for purchases, and your proof of purchase should be on the cards statement.

Some cards, like AMEX will give you a free warranty just for using their card.