Even though you paid off the amount you financed to purchase the weeks, if they have your social security number from that transaction, then they can report your default on the terms of your timeshare agreement to the credit bureaus. However, you can dispute that, and most lenders will take that into consideration when making credit decisions. I'm a retired banker who handled lending and credit administration for over thirty years, so I'm speaking from a place of knowledge.

Walk away; don't pay them another dime.