Mrs. Ansley sends the unheard rebuke to her daughter, Barbara. Mrs. Ansley and Mrs. Slade are on a terrace overlooking Palatine Hill, the Forum, and the Colosseum. They have finished lunch, and their daughter's are going off to enjoy Rome.
Further into the story Mrs. Slade gives some insight into Barbara's character when she reflects that while Mrs. Ansley had been far more beautiful than her daughter Barbara, ". . . Babs, according the the new standard at any rate, was more effective-had more edge, as they say. Funny where she got it, with those two nullities as parents." Then Mrs. Slade reveals that she wishes her own daughter was as vibrant as Barbara.
It is exactly this vibrancy that Mrs. Ansley is rebuking when she murmurs her daughter's name. Her daughter is mocking the two older women for sitting and knitting, as though they have nothing to do. She is embarrassed by the fact her daughter says the girls haven't left much else for their parents to do, indicating that the two women lead dull lives. The irony is their lives were much more exciting than their daughters when they were their daughter's age. We learn at the end of the story, of course, that Barbara Mrs. Ansley's and Mr. Slade's daughter. Seemingly, then, Barbara gets her vibrancy from her father.