Although this story starts with a trip to the dentist, most of the story has nothing to do with our narrator's experience in the chair. It can be assumed that the reason this bit of background is added to the story is that it explains why the narrator and her mother had happened to be in London and in that particular café when they encountered the man whom they came to call "the umbrella man."

As far as I'm concerned, no one ever enjoys a trip to the dentist. However, the narrator shows an acute awareness that the experience could have been far worse than what it was. While the dentist found one cavity, in a back tooth, that needed to be filled, the narrator tells us that the procedure was carried out "without hurting her too much." Given the incredible pain that must sometimes be faced in the dentist's chair, it seems this trip was "enjoyed" about as much as it is possible to enjoy such an appointment.

We are told that the girl and her mother traveled "up to London" to get to the dentist's appointment, and it seems likely that our young narrator enjoyed the experience surrounding her dentist visit, especially as she got to enjoy a banana split after the appointment. Her enjoyment of the banana split also indicates that she must not be in too much pain after the dentist appointment.