The title "A Retrieved Reformation" is probably not a very good one because the word "retrieved" does not quite explain what happens. Perhaps "salvaged" or "saved" or "preserved" would be better.
Jimmy Valentine, the hero of the story, is a professional safecracker. Once he gets out of prison he goes right back to his old ways. But then he meets and falls in love with Annabel Adams and decides to go straight. This is his "reformation."
He changes his name to Ralph Spencer.
At the end of a year the situation of Mr. Ralph Spencer was this: he had won the respect of the community, his shoe-store was flourishing, and he and Annabel were engaged to be married in two weeks.
Annabel's father is president of the local bank. He is showing his new safe and vault to a group of people including Jimmy, who just happens to have brought his suitcase full of his burglar tools along with him because he is planning to send them to an old pal.
Suddenly there was a scream or two from the women, and a commotion.
A five-year-girl named Agatha has accidently been locked in the vault, and there is no way of opening it because "the [time] clock hasn't been wound nor the combination set." The little girl might suffocate or die of fright.
A detective named Ben Price has been on Jimmy's trail since he committed a series of safecracking jobs after being released from prison and before meeting Annabel in the town of Elmore where he was unknown. The detective has followed Jimmy into the bank and is watching the uproar. Jimmy, now a reformed man, decides he must reveal his true identity by breaking into the supposedly burglar-proof bank vault, using his special tools. He knows he is exposing himself to another jail term as well as losing the girl he loves; but he is the only person who can save the life of little Agatha.
Annabel turned to Jimmy, her large eyes full of anguish, but not yet despairing. Toi a woman nothing seems quite impossible to the power of the man she worships.
Jimmy opens the door in ten minutes and frees the hysterical child. He naturally expects to be arrested by Ben Price, whom he knows from past encounters. But Ben tells him:
"Don't believe I recognize you. Your buggy's waiting for you, ain't it?"
So Jimmy is able to "retrieve" his reformation. He is able to retain his new identity as Ralph Spencer, a pillar of the community and the fiance of the beautiiful girl who is the daughter of a wealthy banker.
O. Henry never explains what Annabel and her father thought about "Ralph Spencer" having a suitcase full set of state-of-the-art burglar tools or of his having the expertise to open the burglar-proof bank vault in ten minutes.
Explain the meaning of the title?