Ask them to explain to you how the agreement that was signed is not legally binding. If the deal was illegal for some reason, then you're probably stuck, but it sounds like they just messed up and gave you a deal they later thought they shouldn't give.
That is what happened.
And, as an update, it the salesperson completely backed off when I threatened to complain to management. What I'd been gathering way pretty much right.
My salesperson (in her zeal to close the sale with me) gave me a rebate that she wasn't sure her manager would approve. Her manager apparently didn't approve it (when he was in, two days later), but since she wanted to close the sale so bad she already signed a contract with me guaranteeing it.
Whelp, fast forward two days, and guess what? Manager didn't want approve the rebate. But of course now we've both already signed something saying that the dealership is in fact paying me that rebate. Dealerships apparently have no issue cannibalizing their own employees when things go south, since apparently the rebate is now going to be coming out of my salesperson's commission. Which is what sent my salesperson into a frenzy to get me to resign - better me than her, right?
Ultimately, I would feel a little bad about it - I don't want my salesperson to lose her commission. At the same time, she attempted multiple times to mislead me into thinking that I HAD to resign, and she also brickwalled me away from management, and said some very false and misleading things about whether I could still get tags if I didn't resign. If it wasn't for her consistent dishonesty, vagueness, and unwillingness to even talk about the details of what I'd be resigning with her, I'd have worked with her finding a way so the rebate didn't need to come out of her commission. But I lost my patience thanks to all those issues, and as soon as I made a firm statement that I wasn't resigning and that I wanted to talk to management, my salesperson completely backed off.