Where did it say she manipulated everyone to make him homeless? First she wondered if he went home, and thought it was good as long as he was okay, but then she thought what if he didn't, and went to the park because she thought it was the only place he could be at.
Her feigned ignorance about technology is so blatantly transparent it barely counts as a lie, so it's obvious she's just using it as an excuse, especially since she's trying to use that as an excuse to invite him in.
Also, having a red flag doesn't make someone a bad person. Everyone has flaws, some more than others, and some flaws are acceptable while others aren't.
What I would do in that situation is talk. You know, communicate. Or I'd play along with her game and tease her back if I found myself inclined.