Is it Halachically sound to settle debt for less than owed with a credit card company?
Hm. We have a concept called "it is a mitzva to pay back your debts" (and thus, for instance, if you were looking to liquidate some assets anyhow, you must give your creditor cash, rather than the assets). On the other hand, here the creditor is completely willing to waive the remainder of the debt.
From a strict halachic perspective, if they waive the debt that's it you're fine. From an ethical perspective ... I'd think one should make a reasonable effort to pay in full (e.g. purposely going into debt with a plan of making some kind of deal like this is a very bad idea, for all sorts of reasons), but if someone's really in a pinch, we'd say a waived debt is a waived debt.