I think the Varya visit played out this way:
Geoffrey was responding to her texts enough to lead her on a bit, rather than completely shutting her out like he said he was doing. When the new gf asked him at dinner if he was replying to Varya's texts, he hesitated and looked all shifty eyed, clearly seemed to be lying.
So Varya has just enough response from him to think he's still interested. The TLC producers egg her on, telling her they know that he's just hurt and downplaying his feelings now, but they know he'd really love for her to give him another chance.
Then they tell her they can get her a quick visa, pay for her trip to America (she's said whe wanted to see America), and maybe some kind of appearance bonus payment. Maybe they'll introduce her to some entertainment industry people while she's there and she'll get a job?
She says sure, why not? She's genuinely interested in giving Geoffrey another shot and gets excited about the trip and the fun craziness of suprising him at home -- which the producers have told her would be warmly received, because they know Geoffrey is still in love with her.
In North Carolina, the producers tell Geoffrey they want to come by at a certain time to get some at-home footage with his new gf. So he makes sure the gf is there at the appointed time.
The camera crew leads the taxi to the house and when they get out the dogs are familiar enough with the camera crew folks (and they're old and dopey enough) that they don't get excited or aggressive. They do come to check out Varya but she shoos them off and the dogs figure it's okay because she's with these people they know.
Varya rings the doorbell. Geoffrey answers, expecting just the camera crew. He's genuinely suprised to see Varya, is stiff in greeting her because the gf is nearby. Gf didn't know anything about Varya coming, thought it would be just the camera crew. Her reaction to Varya is genuine, and Varya's reaction to gf is genuine because she'd been led to believe Geoffrey was still pining for her and would be thrilled to see her.
Geoffrey stands there with a grin on his face as he realizes two women are fighting over him. TLC camera crew high fives each other on their successful operation.