you can try https://images.google.com and https://yandex.com/images/ They will catch a lot of stuff. Sometimes pictures are stolen from Latin America Escorts. When you do the reverse search you see.

And yes, you certainly have the right to turn around and leave. Not sure what the "pick up our funds" actually meant as it sounds like you paid before even seeing the girl. If that was the case maybe stay away from those places.

 
But as the other reply mentioned, you should also be checking the pics with a reverse image search and not just taking an ad pic as the truth. Protect yourself because if you're depending on the vendor to do so in this activity you're going to be disappointed a lot.

Don't let your little head make decisions for your big head. Just turn around and leave.

The Asian-orgs are notorious for this practice. They keep making money, so there is no incentive to change plus guys are fearful of being blacklisted if they just leave. I would ask the booker/provider upfront if the pics are accurate and let them know up front that you're going to walk if they're not. If the booker/provider has an issue with you asking, then move on. Plenty of pussy out there.

How are you making appointments with someone with such a paltry internet presence that they could bait and switch you?  

If this is something that happens to you, then you are the one making bad decisions.  

I get that it may often be driven by budgetary constraints, but be an economist about it and consider the true costs.  

Yes, and they are at fault too; I'm not saying they aren't.  

Book someone you know is real.