I'd hammer the nails back out into their side.

Its crazy how many peeps here cant see there are two separate fences with a no mans land gap between. It's really weird because Ive seen this on properties more often then I would've expected I would.

One of the most common scenarios ive seen this is when neighbor A has a pool and put the required perimeter fence for the pool but not at the property line. Also the pool and fence would be installed first. Then neighbor B put up a fence after and told the cobtractor to run their property line. I say contractor because they do as told by person paying, if it was diy fence by owner theu wouldve talked to neighbor and butted the fences back to back w/ no gap. It'd explain the neighbor not caring about the protruding screw out the back because they've never seen a single person between the two fences the entire time they put the fences up.

Other scenarios are quick fix to contain animal till full fence replacing is installed. Or neighbor with bucktooth fence, from the picture angle, looks like they have no sight line to that part of fence from house and said fucked if I care.

Pound the nails out so they’re back on their side. Harmless, but gets the point across(maybe).

Had similar scenario this summer at new house. Solution? We built a 10 ft fence.

Just add more wall when needed.

Does it stop things getting through the fence?

If yes then it's a legally perfect fence.

The screws is probably the only thing that they need to fix up. That's a safety issue but besides that, nothing wrong with that fence.

Edit: on further inspection that fence isn't even on the property line, so it's a non issue.

My guess is there's a dispute of the existing fence, your neighbor wanted to replace it and either you or a previous owner didn't, so they did the next best thing, put up a fence on their side of the property line at a decent enough distance so they could get the privacy they wanted.