I would agree that your choice should be linked to the parts of the story which impact on you the most. I would select from "The Vulture Eye", 'The Madman in the Darkness", "Retribution", "The Pulse" or "The Tortured Man". The last suggestion could be ambiguous: both the old man and the narrator are tortured in the story.
Everyone has his or her own ideas about creating a title for their writing. There is no right or wrong answer for a question like this. A few things to ask yourself if you are asked to come up with alternative titles to works of literature should be:
1. What is the main theme of the work?
2. What are some interesting, arresting passages in the work?
3. Why did the author title the work the way he or she did?
Creating a title is about creativity, sensitivity, and uniqueness. You want to find a title that will intrigue the reader, yet give them a small hint of the contents of the work.
For Edgar Allan Poe's "The Tell-Tale Heart" some alternate titles could be:
* "Under the Planks"
* "The Heart that Would Not Stop"
* "Incessant Beating"
I am assuming this is a creative answer. I would call it "The Eye" maybe.