In the story "Sir Thursday" by Garth Nix, the phrase "My parents are going to kill me!" reflects a character's feeling of anxiety and fear about potential repercussions from their parents. It indicates a situation where the character might have done something wrong or feels overwhelmed by the consequences they might face at home.

However, the response "That seems rather harsh..." suggests a more understanding or humorous perspective, highlighting the contrast between the character's intense emotions and a calmer, perhaps more empathetic viewpoint. This exchange emphasizes the theme of youthful worry and adult understanding within the narrative.