Definitely call the bank yourself and cancel the card.
I found a debit card on the ground at Walmart the other day. That poor woman is probably very upset right now and worried to death. Did I turn it in to customer service? No, I did not. I don't trust them. Did I try to find the person in the phone book? I thought about it, but no, I did not. If someone had used the card fraudulently before I found it, I would get the blame. And it was a pretty common name around here. I might have given it to the wrong person. So I brought the card home and cut it to pieces and threw it in the trash.
I could have called the card company to report that I had found it, but like I said, what if someone else had used it before I found it? I also could have left it on the ground where I found it but I'd like to think I did someone a huge favor by picking it up and destroying it.