For sure I have zero sympathy for Carrier. But this isn't about emotions. You've posted 10x that they "own" it, but you don't know that without seeing the gift deal. From a "legal" standpoint, that's a threshold you're totally guessing on.
Even if you're guess is right and Carrier paid for "perpetual" rights, my question is to what? If the reno winds up like BC Place, the "Dome" is going away. So on your theory, Carrier paid (almost nothing) to put their name on a Dome'd building that isn't going to be there anymore. If the renovation is not (as BC Place was) a gut, then it would be a fact question whether Carrier's rights run to the new building or not. From my seat, if the place is gutted and the walls, seats, turf and roof are all eliminated and replaced, it's not the same building and Carrier's claims go away. Almost certainly they didn't buy perpetual rights to the dirt? At any rate, there are many questions here (and facts) you're glossing over. Good thing you're not repping the University.