I understand you do not want unauthorized or "secret" trails to be shown on OpenStreetMap, however it is not OpenStreetMap's policy to remove unauthorized or "secret" trails. This policy is for several reasons but foremost is because it presents a number of serious safety issues. OpenStreetMap is not just used by recreational users but also emergency responders (Fire & Rescue, BC Ambulance, BC Wildfire Service, Search & Rescue, and others).

The correct approach to dealing with unauthorized trails is to use the informal tag with the value yes. This will result in apps such as AllTrails and Gaia displaying the trail with less emphasis compared to trails without the informal tag or with a value of no.