Hello welcome to OSM. Paths that exist on the ground should not be removed. Please read for more info:
https://wiki.openstreetmap.org/wiki/Why_we_won%27t_delete_roads_on_private_property

The correct way to handle this would be to tag the path access=private, and if there really is a fence cutting the path off, you could map the fence, and cut the trail off where it intersects.

You also removed part of the path that does not seem to be private property in south trail-network. I restored the way, let me know if you need a help making changes.

Removing data from OSM will not stop trespassing & vandals, and purposeful removal of features that do exist on the ground is itself considered vandalism here. https://wiki.openstreetmap.org/wiki/Vandalism