Welcome to OpenStreetMap.

While it may be frustrating when people trespass, the best way to deal with this in OSM is to set the correct access tags, in this case access=private, to the path. The problem with deleting existing features is that they tend to get re-added, without any access restrictions, causing the problem to recur.

Many maps show private paths, tracks and roads, including Ordnance Survey and Google. These maps may not make the fact that it is private explicit, but OSM does.

There is more detailed information on the OSM Wiki here
https://wiki.openstreetmap.org/wiki/Why_can%27t_I_delete_this_trail%3F

I have reinstated the path and made it private in https://www.openstreetmap.org/changeset/163049053