Apparently it's not possible to do this without the sender knowing you took a screenshot. Not much help I guess after the fact but another entry for the uglymugs maybe.
You'd need to ask the escort that. Perhaps she had vetted or trusted the client or they had been communicating already. I don't know the specifics. I don't think using a service like this though is the same as having your face all over the net. There would obviously have to be some level of trust involved in using the service.
However the fact that the recipient cannot keep, copy or pass on the pic would seem to make it a safer way to send a pic rather than sending an email or photo. However, as the General said, one could take a screenshot so not totally secure.
For 99% of people it would probably work fine but of course it's the 1% that you have to watch out for.
Tbh my main problem would be if I'd mostly set up the appointment and the lady sent me her pic and I wasn't attracted to her. Better than turning away at the door but still awkward!!