Time is the best healer of all. If you had have a good relationship with your neighbor, the sourness will eventually diminish. Plus, the argument started through kids, so with all possibilities, it could end up with their initiatives.
Children are less egoistic. Hopefully, your granddaughter will forget everything after a few days. She will again start communicating with your neighbor's daughter. Thus, it will work as an initial icebreaker, and it would be easier for you to patch up than onward. You might get surprised to know that your neighbor was equally eager to fix the situation.