"I might be a bit over enthusiastic about this but I shit you not if I ever saw my cat in a neighbours window, I’d be knocking on their door then and there to get it back."
I often wonder, after my not my cat experience, if I'll ever notice my own cat in a neighbours window. I think I'd do the same, knock, introduce myself and ask for her back.
With my not my cat cat, it started when I noticed she'd let herself in, and was sitting in my sink, pawing at the mixer tap. I was intrigued, so put it on a trickle, and she wet her paw, and started to groom herself, stopping to re-wet the paw every so often. Eventually she was having a shower of sorts at mine, a few mornings a week. I'd put the tap on a trickle, go back 10 minutes later and she'd be gone. I always assumed her owner either didn't have a mixer tap, or there was no one home to turn it on, and that was the initial draw.
Then she made friends with the dog, and roamed further into the house, until she was sitting with me while I watched TV etc. One horrible stormy night, it was getting late and she didn't want to go home, but my cat had come back, and I wanted to shut the window, so I had to carry her home, under an umbrella. I explained to the neighbour she'd been at mine, and that I thought she was waiting for the rain to stop, (but that could have been hours), hence me having to return her. The neighbour just seemed relived she was okay, and had been warm/dry/safe.
It must have played on her mind though, because a few days later, the neighbour sent her bf over one afternoon looking for the cat.
I think they suspected I was locking her in. I took him into my kitchen, where the cat was sitting on the windowsill, in front of the open window, watching the birds in the tree. I explained I leave the window open for my own cat, theirs was letting itself in, and they seemed happy enough with that from then on (once they saw the window was open and the cat was free to leave).
I never fed her (though I would give her a bowl of water, when I was topping up the dogs).