If I pay a credit card settlement, can the issuer legally come after me later to pay the balance?

If you settled with the credit card company or its hired agent, then what you have done by settling for a lower amount is called in contractual terms an "accord and satisfaction". You should put this in writing and have the company attest to it or have the credit card company indicate in a writing to you that if you pay x amount, it is considered a full and final satisfaction of the amount owing. You should also write this as full payment on the memo part of the check you send in to pay it off. If the credit card company or its agent refuses to give you this confirmation, then no your balance will not be considered fully paid off.  If this is a third party collector, you need to find out whether the credit card company has already been paid off; if so, it should reflect on your credit report. Then if the new balance is now with the collection agency, you need to have the agency agree to this accord and satisfaction. Once paid, wait a couple of weeks and write to all four credit reporting agencies to ensure your debt shows paid off or if you wish to have it deleted, file a dispute with all credit agencies it shows up on and ask it be removed from your record.