Hi welcome to OSM. I don't know if this trail really exists on the ground or not, but I wanted to tell you your given reason for removing is not valid.

You have a new account and might not be aware, 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 trails that still exist should not be removed until they are gone. Removing them is actually considered vandalism.

So a trail not being "officially mapped" or "encouraged for use" has no barring on whether or not it should be in OSM. The only thing that matters is if it exists on the ground or not.

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

Read more here:
https://wiki.openstreetmap.org/wiki/Why_can%27t_I_delete_this_trail%3F