yes they can delete the reviews if the reviews are in violation of the websites rules and guidelines and the states laws. in short sites like yelp have their review process. on top of that once the review does go on any one can make a complaint about any of the reviews and the site reviews the post to see if indeed the post is in violation, if so they do delete it.

any treatment provider listed on yelp or other website can also make a complaint to the site and if they choose to take legal action if there is a law being broken. most websites do co operate with court orders requiring them to disclose personal information and ip addresses in situations where a law is being broken.

for example if a treatment provider has a court order against their client and the client is cyber stalking, or other breaches of cyber laws they can go to court and the court can order a website to release information that can help with the court case that the client is in violation of a cease and desist or order of protection.

but in general as long as there is no court orders requiring you to cease and desist/ stay away from this treatment provider all that will happen is yelp will review your review of the treatment provider and if it violates the sites rules it will just get deleted. if it doesnt violate any of yelps site rules then it will stay up for others to see.