May I suggest posting a sign that reads, "Please pick up after your pup! It's YOUR duty to pick up your doody! This bag is a one time courtesy, next time bring your own bag!"
Because that is very rude. I don't worry if it's off to the side in the bushes where we don't walk around anyway, but on the lawn where people are obviously walking is just plain rude and inconsiderate. Maybe head to Lowe's or Home Depot and grab a wooden stake, and a small sign. Some type of permanent marker should be fine to use. Or you can go to dog poop signs.com and have one custom made. Not sure of the price, but you can get them custom or premade. But yeah. That's a rotten neighbor!