I had the same question. Short answer is No, you can not pay your monthly Care Credit payments with your HSA debit card or account. I contacted Care Credit Customer Service to check and they confirmed that in order to make the monthly payments on the Care Credit Card you would need to mail in a payment (check) or link your banks routing number up online. Below is a statement I found on Care Credit's website.
"Please note: Payment by FSA/HSA or credit card is not available. Payments are also not accepted directly at your provider's office as well."
