Quote:
There's no question of Susan having proper parents. Strangely, Ian and Barbara never ask about them, even though they have plenty of opportunities after they first take off in the TARDIS. As concerned school-teachers, they should have shown an interest in her parents and how she was coping without them. Or whether they were still alive, even.
As she's been in the school for some time, this bit would have been dealt with when she first arrived. It's quite possible that the school was simply told that her parents died when she was very young and she has been raised by her grandfather. That's not exceptionally rare. The fact that neither one of them is surprised when Barbara says the reason she can't work at home with Susan is because her grandfather didn't like visitors suggests that they already know he is her guardian, and once they leave in the TARDIS the question of her parentage probably doesn't seem like a top prority when running from cavemen or Daleks or trying not to get their heads cut off in revolutionary France!