My first reaction? Ask to see the plans. Sometimes trees are actually marked to be cut on them. If so that's a design issue and you weren't consulted.
Second reacation? They didn't trench close to that tree and could gave dug in front of your house with a smaller machine.
I deal with this doo-dee all the time. The contractor will ignore you. Go to the town and raise hell. In these situations I represent the town and I'd be on the horn with them asking how we make it right. Horse trade. New driveway apron or an extension of your walkway. Make a stink. Generally the town will make you go away with a freebie.
As for the tree? It won't be fixed and you won't get cash. Demand pavement or concrete. Looking at the project from the pictures, a nice new driveway apron is your go to since they need to pave right by your house. Spending a few extra hundred for Mr. Newton to shut the fawk up and smile is money well spent.