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In California, the statute of limitation on a credit card account (open account) is 4 years from the last activity on the account (charge or payment). If this has been more than 4 years, the debt is not collectible.
This is likely why they are willing to drop it without much fuss. Whatever you do, don't reaffirm the debt by admitting you owe it. IF you admit that the debt is valid, it can reaffirm the debt and cancel your statute of limitations defense.
You can agree to provide them what they ask to get the debt out of your hair, but maintain that the debt is barred by the statute of limitations and that you deny the debt is valid.