Student A has been asked by a Teacher to bring Student B to their supplementary lesson. When confronted Student B remembers that the teacher said something about a supplementary lesson and after failing to escape is dragged to their lesson by Student A.
Upon arrival Student B says
and the Teacher responds
I'm mostly confused with what the ておいて means because I thought ておく could only be used with transitive verbs but 遅れる is intransitive.
I tried figuring out what it could mean and came to two possibilities
"Putting your lateness aside" (Let's bring up your lateness (遅れて) and then put it down (おいて))
"You're late" with the teacher believing that the lateness is intentional by Student B (The being late (遅れて) was put into effect and kept that way (おいて))
But they're really just shots in the dark trying to make some logical sense of it and I still don't understand why ておく can be there.