[NEEDS SAVES] [CD] Stray pets are not labeled as strays when invited to lot

I'm not sure if it's specifically the invite action? It seems like next time I meet a stray I've been befriending, they're never a stray anymore. I need to befriend and adopt in one go, or I miss out... though sometimes the third or fourth time I meet them they're a stray again. I'm just not that patient and usually have picked a different pet by then. But even if it's just going back to the same park I met them in originally, and waiting for them to show up, they'll no longer be a stray at the second meeting. I assumed townies were adopting them.