Your grass or lawn is your private property and you have every right to decide who can be or use your property and who cannot. If someone is seen walking on your grass, despite a warning sign, it can be considered trespassing on your property. Trespassing laws and penalties differ from state to state. You will have to look through your local laws and codes to see what action you can take against the violators. If someone trespasses on your property despite due warning the best approach is talk to them and ask them to leave. If people are constantly using your lawn as a shortcut path, it is better to put up a barbed wire or fencing along the boundary. Legal action can be taken for repeat intrusion and non-compliance.