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Did you actually authorize them to apply charges to the debit card? Implied in giving them the card number is that you reached an agreement to make payments. That likely, if agreed to, would reset the SOL on the debt.
If they have either not sent dunning notice or it has been less than 30 days since they sent you dunning notice, you can send them a formal request for debt validation. While a DV request under the FDCPA does not mandate that they send you validation within any period, it does, if timely, place the debt collector under a cease collection bar until them do provide validation, which includes reporting to a CRA.
Did you receive dunning notice, and if so, when?
I did not receive any notice, and yes, I did authorize them to charge my card (ugh!).
Unfortunately, by talking to them over the phone, you've already given up some legal protections that might be in your favor if you kept all collection activity to USPS certified mail with return receipt requested. I only communicate by mail because it's in my interest to get them to commit mail fraud versus trying to prove in court that they made promises over the phone.
Paying for a collection doesn't help most credit scores, but it also can get rid of a risk of a lawsuit -- if the collection agency is still within SOL to sue you.
Since it's medical, you may have had ten different ways to have it removed from your reports -- unfortunately paying it now means you probably have a payment arrangment made and that's a new legal agreement. It may reduce your ability to get it removed from your reports.
I would suggest just paying it in full now, and then doing a goodwill saturation campaign mercilessly until they remove it for goodwill purposes. That's going to cost some money for stamps, but it may end up getting resolved to your benefit.
Don't ever pay a collection agency or promise anything over the phone without posting the details here first.