Usually when a provider reports a fake review, TER admin reaches out to the reviewer to ask for proof he saw her. Proof is usually an email, PM here or a text exchange. Of course texts can be faked, but it is much harder to fake e-mails. That's why most reputable providers listed on TER have their initial contact by e-mail, so there is a trail. Do you do that? If the accused reviewer never replies, technically TER will usually take the review down, but I think you need to keep on them about it.
As far as being delisted, there are a number of good reasons that TER will delist a provider - LE issues, significant other issues or being outed to name a few. Not being happy with a review, fake or not, is not one of them. Since you have already announced to the world that's what your reason is, TER will likely not delist you, but I could be wrong about that.
All I can recommend is stay on admin for getting proof the guy saw you and if he doesn't respond, then the review should come down. If the guy does send proof, they will let you know and you'll just have to do whatever damage control you can.
So, about those $300 pee fest dates. How much notice do you need for something like that? My dog is into that sort of thing and he's got a birthday coming up.
Just kidding.