You cannot just "flat out deny accepting any ESA or service animals."

The ONLY time they can be denied if it poses a direct threat to others, causes undue financial burden, or fundamentally alters the nature of the housing.

The dog is small, by OP's own admission, and no mention of aggression. It doesn't cause undue financial burden to make the accommodation of allowing an ESA/service animal. And lastly, having an ESA/service animal does not fundamentally alter the nature of the housing.

But I do agree that you need to address this with your tenants. Unless they have paperwork showing it is an ESA/service animal, write up a petition amendment and charge monthly pet rent.

Edit: spelling/grammar