My mom has been letting a neighbor graze her pasture groundSince grazing cattle isn't sufficient to establish adverse possession
I doubt that mowing it is sufficient. Plus your "possession" has not
be adverse to the real owner. And if the real owner wasn't even aware
of this it's not a "hostile" possession. I don't think you have a leg
to stand on. It would be different if you had been using this strip
to access your garage, that could have been considered hostile, open,
notorious, and adverse to the real owner and at the least you might
have a good chance to get an easement to continue such use if the
owner suddenly decided he didn't like you and told you to get off. But
mowing it, ... don't think so...
gratis. I called our attorney to ask what issues that might raise.
Almost his first words were about adverse possession. Then he raised
the liability issue. Questions about who had to maintain fencing, etc.
This is in Nebraska. We have fencing laws and all that sort of stuff