Henry S. Harrison offers many clues along the way that the clergyman and the old woman are the reporter and the criminal. In fact, the author offers so many clues that seem to connect the old woman with Miss Hinch that the reader begins to suspect the opposite must be true. In detective stories, false clues are called "red herrings." Many of the clues seem obvious along the way. Others are revealed after the identities are revealed, leaving the reader to review whether they had noticed it when it occurred.
The extended conversation on the train is the first clue that the clergyman and old woman are the pursuer and her quarry. Their descriptions of having a beard and wrinkles respectively raise suspicion, because those seem like stock items of disguises. There is some doubt raised, however, when other characters get involved in the conversation. One of them might be a disguised character. The author hints that the old woman is Miss Hinch when she defends Jessie so strongly. Similarly, the clergyman's defense of Miss Hinch seems calculated to throw suspicion away from him. In retrospect, however, the reader can see that confusion was part of the author's plan.
As the story progresses, the clergyman suggests that the old woman accompany him, not the other way around. These clues, again later shown to be misleading, suggest that the clergyman is Jessie in pursuit and that the old woman agrees so as not to be suspected.
In the end, it turns out that the biggest clue was given on the train. The clergyman's claim that Miss Hinch was too clever to be caught was her bragging, and inviting Jessie to accompany her was part of her playing with the reporter to demonstrate her own superiority.