if they leave a 2" strip i just mow it. if they leave a 2' wide strip i just leave it there to grow and never move over a single inch. once they see you aren't gonna cut it they will mow it themselves. i think they think they are getting you to cut part of their yard for free like a few inches really makes a big difference.
i have one where the property lines are clearly marked with stakes in the ground. one cut the neighbor stops mowing 2' on his side of the stake and the next time he's 2' over on my customers side of the stake. still other times he does it right and mows right up to the stake. i dont' understand to be honest. i never mow past the stake. if it's clearly marked then never go past that mark no matter what they do.
some of them can't even make a straight line. it will look like an S where the property lines meet.
i just straighten it out for them.