Shbear, did you get the receipt after you paid the debt? Ask them to update your account as 'paid' in your credit report. After some days, pull your credit report online and check whether the account has been updated. If it has been done, the whole process will be complete.
Asking for refund comes later if your account is not shown as paid by the company. If it has been done so far, then you won't have to worry anymore.