Is “they” a civilian dentist?
The military ID Card serves as the medical and dental proof of insurance for all civilian providers. Even with my TRICARE Retiree Delta Dental Plan, I have no policy or group number. I showed my DOD ID card once when I signed up as a patient, my SSN was matched against DEERS eligibility, and that was it. DEERS is Defense Enrollment Eligibility System; your DS is in it. If he gets in an accident, his CAC Card is all the ER needs to bill TRICARE with no out of pocket for him.
Unless things have changed, I don’t think mids can get coverage for orthodontia from a civilian provider, especially if it is strictly cosmetic. They are able to get braces from the USNA Dental unit, though I would guess Invisalign is not covered. Military folks are expected to get their care from their installation MTF (Medical Treatment Facility), unless it is an emergency.
I have re-read your question several times, and I am still not sure what the actual situation is. I am thinking a misunderstanding has occurred. No military dental staff would ask for a policy and group number.
See the link below, and look at Services Provided and the other links, for USNA Dental.
If you look at the Dental Emergencies, it describes under what circumstances a civilian provider can be used.