Mike decides to go the "unobtrusive" route. She told him that he was being too intrusive before, after all, so now he's going to respect that, but leave the option open to her to initiate contact. He takes a seat near her, where she'll be able to see him, and asks for a menu, keeping his voice at exactly the right pitch to alert her to his presence without blaring oh hey, look at me!
He's a man of honor, after all, so he's honoring her request, as much as it might kill him to do it.