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I am sorry to learn of this matter.
The restaurant is incorrect - there is no official agency or governmental body that actually issues ID cards for service dogs. There are a lot of private agencies out there that issue these cards for service animals, but they are not required and businesses cannot require them.
You can report the business to the US Dept. of Justice for non-compliance, complain to the owner, file a dispute with the BBB, or file a complaint with your state's attorney general (or any combination of the above).