I don't think there is a solution to this, other than ignoring them or maybe having a path made where they have already trampled down the grass. Or if you wanted to contact the municipality and see if they could alter the sidewalk.
I would let it go, personally. There are worse things in the world than someone walking on your grass. Like you say they are already antagonized by you watching them.
Just wanted to offer another perspective. Life is too short to make a big deal of small things.
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