I think it comes down to whether the OP feels Cousin is genuinely trying to be generous by paying for the entire gift that has four people's names on it, thus sparing those other three people from having to spend money while still allowing them to bask in Grandpa's thanks; or if the OP feels Cousin is trying to be controlling, kind of rubbing in the other three people's faces that Cousin can afford the entire gift when the other three can't, and setting up a situation where the other three "owe" Cousin for putting their names on a gift they didn't contribute to.
Even if Cousin has the best intentions, she is making at least one of the other three people (the OP) feel uncomfortable about it. It would have been better if Cousin had stuck to the original agreement, that all four people were fine with. At the very least, Cousin should have suggested
she pay for the entire gift (while putting all four names on it), and abided by what the majority of the others felt about that idea. Instead it sounds like Cousin just decided to change the arrangement on her own, without consulting the other three people who were part of the deal. And I think that's rather thoughtless, even if Cousin had good intentions.
I would not try to pay Cousin back by check or surreptitious cash. Cousin has made it clear she doesn't want money from the other three. I think I would go with getting Grandpa an accessory to the gift, in the price range that I was going to contribute to the main item. That way I would feel like I was really
getting Grandpa something, and no need to quibble about whose name is where because all the gifts go together (accessories for main gift).
On a personal note, I think I would be at least slightly irritated with Cousin (more so if I suspect her motives were not pure), and would not feel like getting her a gift to repay her, even a token gift. Personally, I would not feel like she did something nice for me. I would feel like she reneged on an agreement we had made; sure, it saved me some money, but I had agreed to spend that money, and she took that choice away from me. I'm not saying this is a cut direct offense or anything, just that I would understand someone being displeased about the situation. And I can see how for someone else, they would kind of shrug and be like, "Hey, saved me some money, no big deal, thanks, Cous!" I don't think either reaction is unreasonable.
ETA: OP responded while I was typing and seems to have made a decision. Good for you, you know Cousin better than any of us.