I would email and follow it up with a meeting (even if an MS teams meeting) but better to go in with DD there so she can hear & feel your support
There were suggested emails earlier so have adapted now you have information , it is worse than we thought as it was minor untucked short and loose tie at 9pm; Told off on the evening outside school;, Given lines; made to miss part of another lesson ; getting DD in trouble with other teacher due to that. , This is really an overstep by teacher and disproportionate.
Dear Head teacher
Re DD - class xyz - re Mrs X's behaviour outside school
My daughter goes straight to friend A's house on Tuesdays after school for tea then onto their joint swimming lesson, after which they quickly get changed back into their clothes at 9pm and they wait 5 mins in leisure centre foyer for the dad to fetch car to drive friend and DD home.
At this late hour nowhere near school nor anything to do with school, Mrs X a passing teacher approached my DD and friend in this venue and told them off, causing confusion to the girls.
Mrs X insisted on their attending a meeting at 9am following day. This caused both trouble as they missed 15 mins of a lesson with another teacher and Mrs X gave them 50lines to write whilst continuing to berate them. Her complaint was about a slightly untucked shirt and loose tie, as they'd gotten dressed quickly just to go home after swimming lesson whilst still damp. I cannot see this was necessary nor was there any sense of proportion to her actions.
I am concerned about this teachers behaviour outside school hours and at a different venue, towards children who are not in her care at that time, who found her approach intimidating.
If they had been witnessed behaving extremely badly or anti socially at the time, then I would understand a teacher contacting me (as a parent) the next day to discuss and ask we spoke together to the girls. Neither DD nor friend were however behaving in any way other than respectfully as they waited briefly in a safe space at the leisure centre for a lift home at 9pm.
I do not give consent for Mrs X to approach my DD again outside school at a different venue late in the evening in this manner, nor to then later impose inappropriate punishments at school.
Please look into this incident. I would appreciate reassurance that it will not happen again.
Regards
Mum"