Leaving notes on a receipt is a two-way street. Most of the time, it's the customer who leaves the note, but the restaurant can also print whatever they like on there. Apparently, this restaurant uses that ability to provide selective discounts.
We all know where they're coming from with this. It's never fun when you spend money to go out for a meal, and the meal is ruined by young children screaming and running around the tables. This is a nice way of recognizing good parenting.