Can credit card issuers challenge the discharge? 

While credit cards are generally unsecured and therefore dischargeable in a Chapter 7 bankruptcy, there are exceptions.  Credit card issuers can challenge the discharge of their debt in Chapter 7 by filing a non-dischargeability action claiming that the debt should be excepted from the discharge.

Credit card debts can be excepted from discharge for two reasons:

1. The application submitted to get the card was fraudulent, or
    
2. The card was used fraudulently.

The non-dischargeability of "fraud" claims arises only in Chapter 7 cases.  In a Chapter 13 case even debts incurred by "fraud" may be dischargeable.