Credit card - can you charge fee for new card?

Can the bank charge a fee to customers who want to close their credit card and have a new one reissued?
Support services states that they have had a few clients who have given out their numbers to companies on a trial basis, declined the service but the company charged their card anyway. Now they want to close their card. Support services does not feel that the card needs to be cancelledand wants to start charging a fee for this, any opinions?

You can charge any fees you want, unless prohibited by State law, as long as it is disclosed and contracted for properly.

But if you charge them for a new card, don't they have the option of going to a different bank where they could get the card free?

I agree Lois, but it also teaches the customer some responsibility. In the past we never charged for replacement cards. But it seems the same people lose them over and over and over and over...now that we started to charge those same people don't seem to lose them as much!