Park vs Conservation area

We have an area classified on the map as a “park” which is actually a privately held conservation area. Should I change it to a class of “area”?
People see the green outline and think it’s public which is causing trespassing and damage issues. (and nobody reads tags that say ‘private’)
Thanks,

Tycho

(Same question https://help.openstreetmap.org/questions/80405/park-vs-conservation-area))