How is date of last activity defined for a settled credit card debt?

The date of last activity for a settled credit card debt is the date that the settlement check cleared your financial institution and was posted to that credit card account.  As the account was settled, there would be no more activity on that account.  I hope that you have a letter from the agency offering the settlement.  Without a letter stating the amount of the settlement, you may have just made a big payment on the debt and someone else will be hounding you for the balance.