What's the meaning of 遅れておいて

Question

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

さっさと補講とやらを始めてくれ

and the Teacher responds

遅れておいてその態度はいただけませんよ

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.

Answer 1

First of all, (-て)おく as a subsidiary verb can be used also with intransitive verbs. For example, 明日は試合だから今晩はよく寝ておく is a perfectly valid sentence even though 寝る is intransitive. All those subsidiary verbs can be used regardless of the transitivity of the main verb.

おく has several meanings. The best-known is "to do something in advance", but おく in the sentence in question means "to do something and leave/forget it". You may know おく is used like this:

• 彼には好きなように言わせておこう。
  Let him say whatever he wants to say.
• あいつのことは放っておけ。
  Leave him!

In your case, おいて in 遅れておいて is difficult to translate, but it indicates he has done nothing after being late. This ～ておいて is a common pattern used to blame someone for doing something (usually bad) and not worrying about it. Examples:

• あいつは大失敗をしておいて反省すらしない。
• あの人はたくさん食べておいてお金を払わずに店を出て行った。