Synchrony reconsideration: will paying an old PayPal default (off my report) help me get CareCredit?

About 8–9 years ago, I defaulted on a PayPal Buy Now, Pay Later Credit account through Synchrony Bank. It was only about $500, but I was in a bad financial place at the time, fresh out of college with too many credit cards. I never paid it off, and now, nearly a decade later, it’s no longer on my credit report.

My credit today is in much better shape. It’s not perfect, but I have good scores, several established accounts with on-time payments, and a solid job with good income.

Here’s my issue: I keep getting denied for a CareCredit card, and I suspect it’s because Synchrony still has an internal record of that old default, even though it’s no longer on my credit report.

My question is: if I call Synchrony and ask for reconsideration, and offer to pay the old $500 balance they most likely still have on record, do you think they would reconsider and approve me?

Has anyone had a similar experience with Synchrony (or another bank) where paying off an old default helped them get back in good standing or get approved again?