You shall not pass

from here (image source)

You might be like the person who put up this sign and fence and think that the sidewalk there is for people to walk on, but in reality it's only purpose is to keep people off the grass. Take that away and people will be wearing paths in the sod in no time at all. If you don't want people going through the area then you're going to have to fence off more than just the sidewalk.