Final answer:
The question seems to be set within a narrative context discussing the effects of technology on family and the emotional disconnect it can create, rather than a specific event of a carpet burning.
Step-by-step explanation:
The passage you've referred to appears to be from a narrative where there's a significant focus on technology and its impact on family dynamics, rather than a specific incident of a carpet burning. Instead, the narrative deals with stirring themes of technological dependency, parental control, and the emotional turmoil within a family unit whose members are reliant on artificial constructs for their daily lives, such as automated houses and virtual reality nurseries.
Characters like George and Lydia Hadley grapple with the realization that their reliance on technology, which has replaced human roles in their household, has led to a loss of connection with their children and with reality itself. It is this overarching theme that the story seeks to address through various incidents, including the malfunctioning of high-tech amenities and the family's subsequent reaction to these disturbances.
The action of Gerda's parents, or lack thereof, toward a burning carpet (which isn't directly described in the provided excerpts) would be reflective of the narrative's critical look at the detachment and helplessness induced by an overly mechanized lifestyle.