The Doctor doesn’t seem to understand the concept of working for a living. It’s alright for him, he lives in a blue box that can go anywhere and anywhen. He doesn’t have to worry about bills; he doesn’t have any. He’s the time and space equivalent of a gypsy with a mobile home, only his doesn’t need petrol.
Clara, on the other hand, needs her job. She can’t just skip out of class whenever the Doctor shows up.
Then again, these kids are in detention; she doubts they’d mind leaving early.
“Okay, that’s long enough, you can all go home.”