Your lease/trade is a little confusing. If the buyout $37k, and market value is $43k, then you have some positive equity there. Were you just giving this to the dealer, which gives them essential $6k above MSRP right there, or would able to apply the profit from that deal to lower the cost of a new Raptor below MSRP?
Either way, I don't think it was really wise to look at this as a single deal. I get that it needs to be for tax purposes, but I would have negotiate the sale price of the Raptor, and told them you'll decide on the trade value of your existing f150 when it's time, to make sure it's done with fair market value. My guess is that they are getting a lot of profit off your trade in, and this whole endeavor is just to squeeze a little bit more out of you and make you feel like you're lucky to have this deal so you don't back out of it.
As far as them asking for the bed cover, I would have said no. If it's worth $500 to them, then maybe I give them $500 and keep my cover...since it will surely cost you more to replace it.