When a credit card company charges off the debt do you have to pay them back?

Writing or charging off a debt is an accounting entry to acknowlege that the asset they have (the loan) is not performing and that investors/readers of the financials, should not consider it valuable. Again, it is only a required accounting entry - it does not effect your debt to them, discharge it or reduce it in any way. You still owe. And they will...in fact must (to satisfy those same investors and regulators that read those financials), try and collect it or get some value for it.