The same thing has happened to me and I took the card into the branch.

I also called the woman because she was listed in the phone book and left a message that I had found her card and had turned it back into the bank.

I also found a wallet with lots of identification and money in it. I tracked down the owner by phone - he didn't live that far away so I drove it back to him.

I thought he was going to push me right into heaven he was so grateful.
Turned out he was quite elderly and the money was critical for him.

It makes you feel good to do the right thing - but that's not the point - it is THE RIGHT THING TO DO.