This story is "a story within a story." A young man on a train by chance shares his coach with a woman with two children who are bored and fretful. When she is unsuccessful at entertaining them with a conventional and moralistic story, he mentions this, meaning no harm. The woman (actually the aunt of the two children) takes offense, however, and challenges him to try and do a better job of it.
The bachelor does so with bravado by telling the children an unconventional tale in which a "horribly good little girl" is gobbled up by a wolf because her three medals of honour clink against one another and reveal where she is hiding. The chidren an entranced by a tale which goes against the grain of "a decent story," (once again, much to the irritation of the disgruntled aunt). Before saying goodbye, he reminds her that he did indeed keep the children quiet, which was more than she could do.
The climax of the story within the story is of course when the good little girl almost (but not quite) escapes from the jaws of the ravenous wolf; the second one on "real time" is no real climax at all - just another appropriate retort made by the young man before parting company. This rather deflated ending is done on purpose as an anti-climax to take a bit of hot air out of the fuddy-duddy aunt's inflated ego (which it does).
Saki shows by this that understatement can often be more powerful than exaggeration when employed the right way.