I'm so glad your cat is home, and I hope she feels better soon.
It's hard to know what to say to the neighbor. Did she know your cat was considered missing? Some cats simply like to visit neighbors, and do so a lot. The neighbor wouldn't necessarily know the cat wasn't turning up at home.
I'd probably ask the neighbor to stop feeding the cat, and to notify you if the cat is spending a lot of time in neighbor's yard.
How do you feel about keeping the cat indoors? I let my cats go outside for years, but then decided that wasn't safe and kept them in. They adjusted very well. Indoor life for cats is a good thing, especially if coyotes are around.