Let us remember that the conversation that Frederick has with the young woman in the park comes straight after his mother has berated him and left him to pull himself together and to try and control his emotions. There is a deliberate juxtaposition between the way that these two women interact with Frederick and speak to him, and in particular the way that they respond to his tears. From the very first tear that Frederick sheds, Mrs. Dickinson responds in a way that is the opposite of how we would expect a mother to respond:
She whipped out a handkerchief and dabbed at him with it under his grey felt hat, exclaiming meanwhile in tearful mortification: "You really haven’t got to be such a baby!”
The woman, by contrast, clearly differs in her approach. When she asks Frederick about his crying, she is doing it because she is genuinely interested. Her telling Frederick of the story of George, another boy who cries, has such a massive impact on Frederick, even though he may not remember it, precisely because it teaches Frederick that such emotions can be validated and are normal. Having been made to feel for so long that there was something "wrong" with crying and with tears, Frederick by the end of the story is happy because he and his emotions have been accepted by this young woman rather than constantly rejected, which is what his mother did to him.