Tenants boyfriend failed background check, let him on as guest?

Female tenant living alone. I gave her a notice because she had her boyfriend staying there when she was not home. I told her I could add him to the lease if he passed a background check. He did not pass. Now, do I trespass him? Do I have the legal authority to trespass him if he's not causing problems at the park? Or do I continue to allow him on the property as long as she is home? It was a drug offense.