I have seen many posts saying that the restaurant cannot ask whether the dog is a service dog. That is not correct. From the ADA requirements:
Revised ADA Requirements: Service Animals
"
Service Animals Must Be Under Control
Under the ADA, service animals
must be harnessed, leashed, or tethered, unless these devices interfere with the service animal’s work or the individual’s disability prevents using these devices. In that case, the individual must maintain control of the animal through voice, signal, or other effective controls.
Inquiries, Exclusions, Charges, and Other Specific Rules Related to Service Animals
When it is not obvious what service an animal provides, only limited inquiries are allowed.
Staff may ask two questions: (1) is the dog a service animal required because of a disability, and (2) what work or task has the dog been trained to perform. Staff cannot ask about the person’s disability, require medical documentation, require a special identification card or training documentation for the dog, or ask that the dog demonstrate its ability to perform the work or task."
So the restaurant can ask if the animal is a service dog related to a disability but cannot ask what the disability might be although it can ask what special skill the animal has acquired (that would seem to indirectly identify most disabilities)