Hi, thanks for the response. On OSM, we do not removed features if they exist on the ground. If it exists on the ground, it is valid data regardless of a feature being public or private, designated or informal/illegal/unauthorized. Even decommissioned Road/trails that still exist should not be removed. Removing them is actually considered vandalism.

The correct way to handle this is to use OSM's tagging system. access=no would be appropriate if the feature is closed to the public. Once this is done, services that do use OSM data will reflect that and specify their access, and not route anyone that way.

You can add fences for barriers if those exist on the ground to block access to this road. 

Also look into Lifecycle prefix's for the correct way this is handled on OSM.
https://wiki.openstreetmap.org/wiki/Lifecycle_prefix#Stages_of_decay

Please read this for more info:
https://wiki.openstreetmap.org/wiki/Why_can%27t_I_delete_this_trail%3F