This quotation suggests that he (Mr Birling) is trying to protect her from having anything to do with the situation. It seems that Sheila is very protected from unpleasant things like this, and always has been. The Inspector tells Sheila what has happened, and she is shocked. She says, "Oh, how terrible". In an interested way she asks, "Was it an accident?" It is obvious the news has upset Sheila, because the stage directions in front of what she says are, "rather distressed". This implies that she is sensitive, as at that point she doesn't even realise she knows this girl and the audience know that she does in fact know her but cab't remember her and this evokes dramatic irony.