Hello welcome to OSM. You might not be aware, on OSM we do not remove 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. Removing them is actually considered vandalism.

The correct way to handle this is to use OSM's tagging system. access=private, or access=no would be appropriate here if they are closed to the public. Once this is done, services that do use OSM data will reflect that and specify their access.

Please use the tagging system if you believe features are closed to the public. Thanks

Please read this for more info:
https://wiki.openstreetmap.org/wiki/Why_we_won't_delete_roads_on_private_property