I don't see anyone telling you not to respond so I'm not sure where you're getting that.
What would a strong unflappable woman who was unconcerned do? She'd probably respond if she saw he'd texted her. Maybe not right away - whenever she happened to see it.
She would not, however, be contacting him because of the time. She'd be so wrapped up in going about her business, she wouldn't notice if he wasn't there.
