The answer to your question is a qualified no.
Each electronic payment transaction stands on its own and must be authorized by you as the account holder. Even so, it is possible that you previously signed an advance consent permitting your dentist to charge future account payments to your card.
Ask your dentist for a copy of what you signed. Talk to him or her about the account terms so you know what to expect in the future. Because you say you disagree with the particular charge, you notified the card issuer in writing and requested a reversal of the debit. Ordinarily, it should be your choice to pay the account electronically or by personal check.
This answer is provided for information purposes only. It should not be relied upon as legal advice which can only be offered to clients in an office consultation setting when all the facts and circumstances can be fully considered and reviewed.
As a general principal, no it is not legal to take a payment from a check/debit card or a credit card without authorization, however, unless this cause you to incur bank charges for overdrawing you account, I would not get in a hissy fit. The amount involved is not worth a lawyer's time or your aggravation.
I would call the dentist, as you did, and advise the office staff that this is no longer permitted.
I suspect that papers you signed when you became a patient allows the dentist to charge your card for the co-pay or balance unpaid by your insurance.
If this not suitable to you, you always have the option of changing dentists.
The foregoing is not intended to be legal advice upon which you may rely as I have not been retained for this purpose.
I agree with my colleagues that as a general matter, the dentist has no right to debit your account without your express written permission. However, some of the paperwork you signed may have contained that authorization. If that is not the case, I might not trust my dental healthcare to someone who treats you so disrespectfully and in contrast with black letter law.
The answer rendered here in no way constitutes the creation of an attorney-client relationship between the question asker and the attorney answering the question. In order for such a relationship to be created, we will have meetings together and will sign a retainer document.