Your grandma might have had a chance in court depending on the exact situation.
If there are tree branches growing over her property, then most of the time the neighbor is forced to cut them after is is notified about it.
If its just a few leaves getting blown over by the wind then chances are rather slim, but its still possible she would win. Depends on your jurisdiction, here it has to be a severe impairment of her ability to use the property.
