To quote from the novel:
"Still trying to convert me, Cordelia?"
"Oh, no. That's all over, too. D'you know what papa said when he became a Catholic? Mummy told me once. He said to her: 'You have brought back my family to the faith of their ancestors.' Pompous, you know. It takes people different ways. Anyhow, the family haven't been very constant, have they? There's him gone and Sebastian gone and Julia gone. But God won't let them go for long, you know. I wonder if you remember the story mummy read us the evening Sebastian first got drunk – I mean the bad evening. "Father Brown" said something like 'I caught him' (the thief) 'with an unseen hook and an invisible line which is long enough to let him wander to the ends of the world and still to bring him back with a twitch upon the thread.' "
Or, to quote from the Father Brown story itself that is made reference to ("The Queer Feet")
"Did--did you steal those things?" stammered Mr. Audley, with staring eyes.
"If I did," said the cleric pleasantly, "at least I am bringing them back again."
"But you didn't," said Colonel Pound, still staring at the broken window.
"To make a clean breast of it, I didn't," said the other, with some humour. And he seated himself quite gravely on a stool.
"But you know who did," said the, colonel.
"I don't know his real name," said the priest placidly, "but I know something of his fighting weight, and a great deal about his spiritual difficulties. I formed the physical estimate when he was trying to throttle me, and the moral estimate when he repented."
"Oh, I say--repented!" cried young Chester, with a sort of crow of laughter.
Father Brown got to his feet, putting his hands behind him. "Odd, isn't it," he said, "that a thief and a vagabond should repent, when so many who are rich and secure remain hard and frivolous, and without fruit for God or man? But there, if you will excuse me, you trespass a little upon my province. If you doubt the penitence as a practical fact, there are your knives and forks. You are The Twelve True Fishers, and there are all your silver fish. But He has made me a fisher of men."
"Did you catch this man?" asked the colonel, frowning. Father Brown looked him full in his frowning face.
"Yes," he said, "I caught him, with an unseen hook and an invisible line which is long enough to let him wander to the ends of the world, and still to bring him back with a twitch upon the thread."
-The Innocence of Father Brown (1911)