Need to change the shape of a path? Click somewhere on the path with the Pencil tool, and begin drawing. The path will incorporate your revision.
This is also a gotcha.
Drawing across or very close to an existing path makes Illustrator combine the new and existing paths, often to the user’s consternation. The solution is simple: Hold the SHIFT key as you begin to draw to initiate a new path independent of, and without altering, any other nearby paths.