The expression is 'go the extra mile'. And you're almost right - it means that they spend extra effort to be helpful when they don't have to be. Like, if I asked a librarian for books by an author, and they not only gave me what I wanted but recommended similar authors, that would be going the extra mile to be helpful.

What does ''They go extra mile to help you" mean? to make more effort than is expected of you We often use this expression if we want to help others that are needy.