A careful reading of the story reveals the way in which the title of this excellent story relates to Elizabeth's gradual awareness of the true nature of her relationship with her husband. We are told early on in the story that she has associated the scent of the withering but colourful and beautiful chrysanthemums with the stages of her relationship with her husband. She says to her children that in her relationship with her father she has been a "fool." It is only after her husband's death that she comes to realise that the smell from these flowers is really the scent of death. Just as she realises that the odour of the chrysanthemums is related to death, so she comes to realise when she cleans her husband's body the essential and massive difference that lies between them which could never be bridged.
The change in Elizabeth's perceptions of the odour of the flowers thus is explicitly related to Elizabeth's changing understanding of the difference between her husband and herself, and her recognition of the essential differences between them, both based on gender and social class.