If you feed them they will come haha.
Seriously though, cutest problem ever.
Boy, you aren't kidding. There's a bird feeder in the back yard of the rental we're in. It's been empty since we moved in. There were still some dregs in it, and the occasional finch would come by and grab something.
Well, on a whim, I went out and bought a five-pound bag of feed on Saturday and filled the hopper. It went from ghost town to Times Square in about an hour.