Was away at the weekend so missed the fun. Being familiar with the path, much of what has been said didn't ring true. Before responding I decided to head up there today just to make sure I had it straight.
The other end of the track starts at a gate of the main tarmac access road to Edenmill. There is a accesible gap next to the gate and no signage. About 10m further on is a 8ft fence with stile (one of those Grade 2 stiles where a rope may be advisible
), but what I assume was a gate has been removed, so no obvious barriers here either to deter the intrepid. The path then wends it way through trees, some natural and some that look planted, but nothing that looks inhabited or private. This is clearly not a heavily used path. There are no obvious boundaries or change of ownership on the path. There is the same 8ft fence at the other end leading to the private road, but with a padlocked gate. At no point so far, and this is important, has the offending house been visible. The fence only extends for a short distance left where it can be crossed. A quick glance as I passed the house would suggest there is no way of entering the garden from that side without obviously tresspassing.
Assuming at least one set of folk have entered the rear garden of the house. The most obvious way this happened was that on seeing the padlocked gate and not looking far enough to the left to see the downed fence, they have tried to get to the main road through the trees rather than take the 30 minute detour back via Edenmill and have entered that way.
I have a degree of sympathy with folk living in the small number of hill areas within 5 miles of Glasgow over the last year. But only where a similar sympathy and understanding was extended to us Weedgies on the other end of that bargain. It is entirely possible that the homeowner has had some unpleasant experiences but this has nothing to do with the path. The padlocked gate is incongruous as barring access out makes no sense from that side, which is why I am OK with crossing the fence. As mentioned, by locking the gate and removing the stile you possibly force folk to try and get round, not knowing a house is there. Law of Unintended Consequences and all that.
Assuming the land ownership mentioned is accurate, there would be much to recommend that the padlock is removed, allowing people to use the path of least resistance that disturbs no-one. As shown, anything else will simply make the route more visible or give folk more of a reason to go off-piste.