My neighbor decided my backyard birthday party for my kid was actually a community event

My daughter turned 7 last weekend. Small party, maybe 10 kids from her class, some parents, food, a little inflatable pool in the yard. Normal Saturday afternoon stuff.

About an hour in, my neighbor Karen from two doors down walks through my side gate with her three kids. I didn't invite her. I've spoken to her maybe four times total since we moved in two years ago. She had a gift bag.

I was so caught off guard I didn't say anything in time and suddenly her kids were in the pool and she was helping herself to the food table. I pulled her aside after a few minutes and asked, genuinely confused, how she knew about the party. She said she could hear the music and "figured it was open." Our yards are not connected. She walked through my gate.

I told her it was actually a private party for my daughter's class friends. She looked at me like I'd said something unreasonable and said "but there's plenty of food" which I genuinely did not know how to respond to. I said I was glad it seemed that way but it was still a private event. She asked if her kids could at least finish in the pool.

They stayed for another 40 minutes. She ate two plates of food. Before leaving she told me it was "a really nice setup" and that I should "do this again sometime and actually invite the neighborhood."

My daughter didn't know any of her kids and kept asking me in a whisper who they were. I had no good answer.