What's the rules regarding an appointment regarding a UTR.
Then this UTR becomes advertised by an agency? Can we then write a backdated review?

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You have to be careful in a case like this.  The lady may still want to be UTR, despite an agency "outing" her.  There are one or two agencies that consistently "out" UTR ladies and some of the ladies have gotten very upset by it.  They get even more upset when reviews start to appear.  I once commented on one actress who wanted to be UTR despite her agent posting an ad here on TER, and got into some trouble for it, being put on "moderation" for a time.

The bottom line is, make sure she is no longer UTR before submitting a review.  I'd say if she is repped openly by  TLC or Pam Peaks, then it's probably ok.  If it's Lourdes or Perfection Models or another agency... I'd say get some verification that it's ok to post a review.

As for backdated reviews, the session has to be within the past 3 months.  See the link below for more info.

Agreed. I've gotten to where I don't write one for any provider unless I've gotten her OK to do so first. I've only been told "no" once, oddly enough by a very "over the radar" provider. There's been a couple of times I forgot to ask, which means I just didn't write one.  

It seems like there's too much drama over this kind of stuff lately, so I've made it my policy to ask.

When in doubt - don't post a review.

I think you will do best by asking the lady if she wants one. Easy enough to do in the session.