SPOILER: Show
(she is the one talking here)
Without any proof at all besides this scene, I've come to think that maybe this person is very important to the story:
Could the puppy lady be the one who killed Kaji?
Edit: I haven't seen the show in many years (I like the rebuilds a lot because they're shorter and easier for me to watch) so forgive me if this is a known + semi important character