What is the author's purpose in arranging for Vera to greet Nuttel by herself?
Vera couldn't tell Framton Nuttel her preposterous story if anyone else were present. It is understandable that her aunt might have sent her to greet the visitor. The girl is being groomed to become a country wife and hostess, since those were about the only occupations available to girls like Vera at the time. She is supposed to practice being nice to a visitor. But Vera is independent, rebellious, and bored. She takes her feelings out on poor Framton Nuttel by setting him up to get scared half to death when the same inevitable scenario replays itself yet again. Her aunt will start dithering about bird-shooting. The three hunters will return at the same time. One of them will sing, "I say, Bertie, why do you bound?" But Framton will think they are ghosts because he has been set up by this precocious and mischievous girl.
Vera is an actress as well as a storyteller. What really makes the nervous visitor panic is the look she fakes when she sees the three hunters heading for the open window from outside. Saki has previously described her as "very self-possessed." So the contrast between her former self-possession and her sudden goggle-eyed, open-mouthed horror is all the more striking on the face of this pretty fifteen-year-old girl. Naturally Vera's aunt doesn't see this look because the older woman is looking at the three men she has been expecting to arrive promptly for tea.
Framton shivered slightly and turned towards the niece with a look intended to convey sympathetic comprehension. The child was staring out through the open window with a dazed horror in her eyes. In a chill shock of nameless fear Framton swung round in his seat and looked in the same direction.