Dog ownership and what constitutes it? Update.

Made a post about this back during the summer maybe and couldn't find it. Basically my sister dog sitted a dog in Jan and then again in Feb both times returning the dog after 2/3 weeks of keeping the dog. Then around mid March another call came from the mother of the owner of the dog and said they'd need to permanently re home the dog, did she want him. She sat on it for a week, the mother calls back and says do you want the dog cause if not they were most likely going to place the dog at a shelter where he could be possibly adopted etc. So, she takes the dog in permanently in early April. Around July out of nowhere the woman wants her dog back. They were rejected as my sister, her husband and son were attached and spent alot of money bringing the dog back to normal health at the vet and got him chipped etc. He had several issues in the beginning that needed attention. Then it went silent for 6 months until today. A sheriff deputy showed up at her door with the lady wanting her dog. My sister showed proof of ownership with the chip card and doctor bills etc. She also explained that the dog was given to her and haven't heard from this crazy woman(she got issues) who cant even keep her own kids cause she has problems to boot, in 6 months. So they go talk to her and she leaves. My sister told the deputy to tell her if she showed up again and came onto her property she would have her arrested. My sister told this woman "take me to court" you wont win.

We don't deserve dogs. The dog is a sweet boy and a smart one.

Opinions? Does this woman have any ground to stand on? Her excuse is she is "back on her feet" bs. Thanks in advance.