The plot of the story hinges on a nameless and hungry young woman who asks the very wealthy Rosemary for the price of a cup of tea. Rosemary finds this extraordinary and thinks it will be an adventure to take her home:
Supposing she did do one of those things she was always reading about or seeing on the stage, what would happen? It would be thrilling.
Rosemary is clearly more interested in collecting the young woman as an object than seeing her as an individual. She doesn't ask her name and thinks of her as "that dim person beside her."
Rosemary, when she gets the young woman home, gives her tea:
She plied the poor little creature with everything, all the sandwiches, all the bread and butter, and every time her cup was empty she filled it with tea, cream and sugar.
Yet to Rosemary, the girl is simply another pretty object, a substitute for the expensive box she didn't buy. It is as if the girl is the cup of tea.
When Rosemary's husband, however, sees the young woman, she becomes a human being. Having to introduce her to her husband, Rosemary learns for the first time that her name is Miss Smith. Once Miss Smith is shown to be prettier than Rosemary—"astonishingly pretty" Rosemary's husband calls her—Rosemary's view of her changes. At this point she is competition, and therefore, not Rosemary's cup of tea. Rosemary gets rid of her and decides to buy the "fascinating little box" instead.
So being asked for the price of the cup of tea sets the story is motion, and at the end Miss Smith turns out not to be Rosemary's cup of tea.