Um, I didn't really like how she said "they were dating" as an excuse. For me, it seems lame to say it especially when you're still not close to that person, it is a typical line like I've already heard of that countless times (it can be cringey depending in the situation), and it may likely to stir some another drama. Like the guy seems to be popular, and making that kind of reason/excuse seems to be like putting water in the oil.
She could professionally say that "it's invation of privacy", "it's in the job's rules", "please respect our employees' wishes" with a smile and bow, or she could also bring up that she's the daughter of the owner and that's how their shop/job works, and therefore has an authority, in a way (right?) 🤔.
Overall, I just thought that she could do better than saying "those lines". It could also be rude from the guy's part like that excuse may stir up some rumor + attention in his school, which may add to his own problem. But he's okay about that though 😅. Oh well, welcome to the world of shoujo 🤷🏻♀️.