Moorings require a permit, per
https://www.nh.gov/safety/divisions/...rings/faq.html
The mooring must have a decal on it; otherwise, it's not properly permitted and can be removed.
This article implies that abutters may object to a permitted mooring:
https://law.justia.com/codes/new-ham...ection-270-61/
Perhaps your best course of action is to contact Marine Patrol.