We're not deleting private property paths on OSM for a number of reasons. One is that OSM is used by emergency services - e.g. a missing person might have traveled along a private path and knowledge about where those are can save lives. Another reason is that if the path is not in OSM it will sooner or later get added by someone - better to have it in OSM marked private than not to have it. The path will be reinstated - please refrain from deleting it again. If you are worried about AllTrails insufficiently marking private trails, please take that up with AllTrails.