You don't want to hear this, but you are PHENOMENALLY lucky.
DD is in a school where a misdemeanour this small is picked up on and punished immediately, first time.
I've been in schools where so many children don't bother to bring in their book/pen/planner that the teachers would need several hours just to fill in the detention slips. So they don't.
My son is in a school like yours, where children get away with nothing, he doesn't realise how lucky he is.
of course it is a shame that she is upset, but just point out to her the advantages of being in a school with such high standards. With my son, he is the type that would always slack as far as he could without consequences, and luckily for him, in this school it is not very far at all. Your daughters class mates would be far worse behaved in under a different regime.
And this time next week, the teacher won't even remember which children they had in detention this week, without looking it up, so no, she won't be picked on.