As mentioned, the state is important. In CA many kick-out orders (at the end of the eviction process) include an order to stay off the property. If this person was actually evicted by a court order, you may want to read through it to see if it states he cannot return to the property at all. No court order means no strict prohibition.

I believe that in most states - if not all - an invitation from a lawful tenant will render any trespass admonition by you (management) moot. You may then take the issue up with the tenant who is inviting the unwanted guest and it could be that you might be able to take action against those parties that permit him to return ... depending on CC&Rs, lease agreements, etc.