Many people are confused when they get a copy of their credit report and see a collections for "Medical Payment Data". This is seen when someone obtains their credit report with a third party involved, such as applying for a mortgage or at the car dealership. This would not be shown if you were to obtain your report on your own without a third party.
When you see Medical Payment Data on your report, you do not contact them. Because in reality there is no "them" to contact as it is just a term denoting a medical collections on your credit report.
This is done in order to protect the individual's name requesting the credit report, due to federal privacy laws. What your next step would be is to call the credit bureaus that list the collections on medical report. When you call the credit reporting agencies, they can inform you who currently owns the debt.
Once you receive the information from the credit reporting agencies you can contact the medical collection agency directly. This is because they are the owners of the debt and the hospital is out of the picture now. It is not fully known how the credit agencies treat different debts, but it is thought that hospital debt is not as bad on your credit report.
Certainly if you are working with a human reviewing your application such as at a small bank or car dealership you may have some leeway with having medical payment data on your credit report. This is because it may show you had extenuating circumstances. This especially helps when no other collections are on the report.
If you feel this is harming your credit profile you can work with the collection agency in removing the bad mark off of your report. Usually the longer it has gone unpaid, the worse it gets, to a point. When a collection is a few years old it has already done its damage. If you can pay the collection agency right after they obtain it from the hospital you may be able to avoid it going onto your credit report at all.
The older the debt is, the more, the less you should offer to pay off the debt. A debt that is multiple years old you only may offer a fraction of the original bill. If the debt is new, you may pay the full amount or close to it. The best thing to do is have the ding completely removed, this would help your score the most. If not you could at least have the bill on your report marked paid in full.