A customer made a claim of fraudulent activity for a satellite service. He said that the information was taken while he was in the hospital by his roommate. Now, he is claiming that charges for satellite internet are fraudulent but the company had been debiting him since late last year and it shows as a recurring item.

We are going to try to file a claim. Can we deny the customer a new debit card?

Sure, you can always deny a new debit card. There is no "right" to a debit card.