So the new path of the fence (following the decision of the Israeli supreme court) goes within 100 meters of Mevasseret Zion (report).  Mevasseret is a large suburb of Jerusalem just off the TA highway.    One time I went off-road biking from Jerusalem to the reservoir area (which is very close to Mevasseret) and our experienced off-road biking guide/wire service journalist told us that we are actually quite close to the Green Line and that sometimes shepherds from nearby Arab villages come by.