Am I responsible for lawn damage to a home over 1/4 mile away (1/2 km) caused by a truck delivering construction materials to my house?

I live on a relatively narrow dead end road. A large delivery truck just dropped off construction materials to my home. There is a turnaround near the end of the road to accommodate school buses and other delivery trucks but this one was big, really big, and it had a fork lift attached to the back.

After the delivery we watched the truck drive down the road and saw it attempt to use the turn-around. I’m guessing he had to drive on part of the neighbor’s lawn located in the Town right-of-way. Since everything is now snow covered and muddy he likely made quite a mess.

I will probably offer to fix it but I was wondering who should fix it.
Should I forget about it? Is it up to the neighbor to figure out who did the damage? Who is responsible?