They can always ask, but I doubt it. It's a long-term deal newly inked. They don't have a lot of leverage.
I think it was Reiss who mentioned that Amendola could have sat out a lot of games this year with that injury, maybe even called it a season. He didn't. Just coming back in that Buffalo game and playing at the level he did, while in such obvious pain, shows me something.
I doubt the Pats want to be that team that panics at the first sign (season) of trouble. But hey, they've surprised me too many times to pretend I know what they'll do, honestly. If Brady wants Amendola gone, he's likely gone, right?
On the other hand, I do think they'll ask Tommy Kelly to restructure, and I think he'll do it (and I think VW will, too). Kelly's on his last deal, likely, and isn't happy about losing half the season with that knee - all of his rehab was at Gillette...and he said all the right things. He's on the wrong side of 30 and trying to come back from a second ACL surgery.
EDIT: After reading Miguel's update...now they have more leverage than I thought, so yeah, they might well ask for a restructure...and if so, probably one with performance incentives attached.