Middle ground Dido. Middle ground.
You don't assume that either he is a weirdo or he isn't.
You keep an open mind and leave the for door open for your DD to tell you if he does do anything. Anything which again could be brushed off 'oh he's just being friendly!' or whatever.
It worries me that so many people can't see any middle ground between 'sack the perve' and 'she fancies him and is a gossiping bitch'.
When it comes to children and people in authority you need to be careful. Keep communication lines open.
Because CSA starts with the subtle. And the children who aren't given the tools (talk to me) or are laughed at (you just fancy him!) or are dismissed (obviously he looks at you he's your PE teacher) are the ones who do not tell if anything starts to escalate. And by then. He's got them, hasn't he.
I can see zero harm in saying to DD. Thanks for telling me. Does sound a bit unusual. Let me know if anything else happens. Keep an eye out for your mates.
Who is harmed by that? No one.
Who is helped? Well if things are dodgy, children are helped.
When I was a girl we were taught to 'laugh off' inappropriate behaviour from men. That it was just how it was and not a big deal. Throw into the mix an authority figure, and parents who essentially say, I don't want to hear it. And that's go time for the small (ish) number of men who are predatory.
The situations where boys and female teachers are involved have a slightly different dynamic, that the boy should consider himself lucky. That also acts as a hard stop on talking to anyone who might be able to help.