What is the role of Holden's parents?
Holden's parents are simultaneously rather minor but also important figures in Holden's life. They do not have a significant role to play in the story of The Catcher in the Rye directly, but the impact they have made on Holden is relevant to the reader's understanding of Holden's character.
Holden is the narrator of the novel, so everything the reader knows about his parents has been filtered through Holden's eyes and experience. The reader learns that his parents are affluent, and therefore, Holden has not likely struggled much financially; but, Holden's parents are also grief-stricken and, it seems, unable to cope well with the death of Holden's brother.
The reader must imagine Holden's parents and their situation, which also gives the reader an opportunity to interpret Holden for themselves. If the reader sees his parents as cold and harsh, perhaps Holden can be understood more as a victim of his circumstances. On the other hand, if the reader sees Holden's parents as confused and upset by a serious tragedy, then perhaps Holden can be viewed more as a spoiled adolescent who needs to mature in order to understand that his parents are struggling in their own right.