@colorblindcowboy You might find out your neighbours are stressed and would like to better care for kitty but just can’t.
Maybe I’ve watched too many Dodo cat and dog rescue videos but many of them have had serious but respectful conversations with pet owners about giving their pet a better home.
Even if it’s not you maybe if your neighbours are willing to release their cat you could help find a new home.
Maybe a local shelter has some advice on how to do that without taking kitty until it’s safe to do so.
Whatever you choose to do it’s a really caring thing you’re doing to help keep kitty healthy and cared for. I hope it works out one way or the other.