Surveying rights?

Location: NC

I live within city limits in NC, close to a road. The city is having extensive surveying done around my property. I believe they’re surveying for property lines, drainage, and utilities (but I’m not sure, because nobody will tell me? Both the city and the survey crew have said “I dunno”) I have a recent survey of my property lines, so I’m not surprised by any of those markers.

My issue & question is what rights does the survey crew have to come onto my property (like fully in the lines, not in any setbacks or right of ways), and move my items? They’re all over my front and back yard, hopping fences, moving pots and furniture to set up their equipment. They’re also using their feet to kick up chunks of grass. The items they’re moving aren’t even for flagging anything, it’s for their tripods and they don’t put my items back when they’re done. There are multiple muddy holes all over my yard from where they’ve kicked up the grass to set tripods. When they do flag, they’re just picking up random sticks from my yard and tying flag to it.

I’m really really not a “get off my lawn” sort of person, but nobody will tell me what they’re surveying for and I’m getting kind of annoyed at this point. If I’m totally off base I’ll sit down and deal with my muddy holes, but I’m just curious if they have specific access rights that include moving things and digging holes for equipment.