Mo provided the spirit body, so that swordsman ghost of that day probably stuck himself to the mc or the sword and in the missing 3 months they made a deal... quite idiotic to skip that btw...
Beibei has no idea about the ghost swordsman, she gave him the cat merely because she deemed it funny, she had no idea that the mc would be stuck with it.
How weird, that not even the scanlator seems to get the story...