Okay so I'm going to try to explain this as best as possible...
I just recently opened a set on facebook with a girl I knew back in high school that I haven't seen or talked to in over 3 years. She's an HB10 and a college cheerleader so the game I ran had to be nearly immaculate. I ran a pretty good set and number closed her. Then texted her a couple of days ago and continued with some day 2 game, things went about as well as possible...Now here's where the situation gets strange. She posted an add on the internet, selling a tv for her dad. Nice tv and I figured I could finally run game on her in person, so I bought the tv. When I got to her house to pick it up, I mostly interacted with her dad and she barely acknowledged me. Of course we talked some but just small talk bullshit. Then I left without even hugging her or really giving her any IOIs (AFC mistake I know). Finally once I got home, she called me and told me that I left the tv's remote behind. We agreed that I would come by her house again tomorrow to pick up the remote. So what I need help with is, since this is pretty much my last chance with this girl before I blow the set, what techniques should I use to try to recover the set when I go to her house tomorrow? How should I open? What are some lines that would be good to use for this situation?

First of, I think buying the TV is a mistake. It shows that you're jumping in her hoops and she controlls the frame. I know it might seem like a good oppertunity to see her in person again, but you can't really go anywhere from there. Like you said, once her dad gave you the TV you are kinda in a awkward spot since they expect you to leave now.

Ok, now to get unstucko from this situation.

I don't know any of the logistics, like how far she lives from your place etc. But I think going over to her place again will kinda be the same situation like earlier. If you can, tell her that you are busy and can't really make it to her place. ( assuming she lives with her parrents. If she lives on a student dorm i'd defo go to her place! But again, dont know much about the logistics) Tell her something like, ill be in town doing blabla and have some meeting just some bullshit on how you are busy but you COULD meet her up in town since you have to be around there anyway. If she agrees to, just meet in some bar/cafe and work your game!