Take the kitty. S/he's adopted you! They have been comforted by your presence! If you take in the kitty now, you can train her/him to be the loyal lap cat you never knew you needed. You can get her/him to come when called, play silly games, and have her/him waiting at your door for you to come home, at which point they will be ecstatic!
People don't know how to accept unconditional love these days.