This is a page dedicated to theories regarding how the white knights were perhaps punished at the end of episode three.
Karen: "Bad girls will be punished."
Eri: "Like she said, we'll punish them. If not, then I'll let you do whatever you want with them, Captain." - Eri, perhaps hinting at theory # 1.
Theory 1: The white knights were raped. Evidence: Eri suggests to the Captain (a presumably straight man) that he has her permission to "Do whatever he wants with them." Only a handful of things come to mind when a man thinks of being able to do anything he wants with a girl. Since it would be a forcible punishment and the White Knights were on the opposite side of the conflict, any sex would most likely be non-consensual or with the girls knocked out.
Theory 2: The white knights were spanked. Evidence: In the final scene, they are all shown with their heads down and buttocks pointing up in full view. The White Knights' dresses are around their stomachs, which implies that they were pulled up, perhaps for a better view of the young ladies' businesses.
Theory 3: The white knights were humiliated. Evidence: Perhaps it's punishment enough that the once proud and powerful White Knights are now reduced to passive young ladies with their rears exposed.
Theory 4: The White Knights were paraded around. Evidence: A common source of fanservice in Aika Zero is the carrying of White Knights over-shoulder with their dresses flipped up and panty-clad posteriors on full display. This is both humiliating and a great source of fanservice, making it a possible punishment idea.
Theory 5: The White Knights were repeatedly shot in the butt. Evidence: Karen did this to Kana and Rin when they were waking up on the metal slab to put them back to sleep. Perhaps a fitting punishment for the White Knights would be for them to be used as a pseudo-whack-a-mole game for Karen to shoot back to sleep.
Theory 6: The White Knights' had their panties pulled down. Evidence: Eri is quite partial to lesbionics. It would make sense if she wanted to take a look at the young girls' "beautiful skin" in greater detail.
Theory 7: The White Knights were made an example of. Evidence: Aika Zero takes place in an all-girls' high school so showing the other school girls what could happen for rough housing on campus, consorting with aliens and cheating on exams might improve behaviour.