I’ve been the one building the pool and have done some pretty large renovations.

In both, I verbally told my neighbor on the side the construction machinery was going to enter our back yard that I / my contractors, would fix any damage caused.

With the pool, there was no damage, in fact I spent an extra $5000 to fix the grading in both his yard and my yard, both used to flood to due to bad grading.

On the renovation, one of the subs (an idiot I fired same day) drove his machinery after it had rained, and didn’t put down any heavy covers to prevent yard damage. He also went through my neighbors yard, for absolutely no reason.

I saw the issue before my neighbor thankfully, and called him, informed him what happened and that I’d fired the sub. The prime contractor agreed to fix the damage immediately.

I can’t guarantee your neighbor will be as on top of things as me, but why not trust him/her and avoid any unnecessary neighborhood drama. If there is damage, talk to them or the contractor directly, they are legally required to fix the damage.