The past doesn't exactly haunt people in Atlas Shrugged; it's probably more accurate to say that it comes back to bite them in the butt. Characters are always regretting past actions or eating their words. Dagny, for instance, has a bit of an awkward moment when she finds out that the man she swore to kill is actually her true love and soul mate.
But a character's personal history is also a source of strength, pride, and character foundation. Dagny and Hank's pasts in particular largely define who they are in the present. Their pasts helped form the values they currently live by.
The past and memory also are connected to broader ideas in this book. Historical decline and the idea of time moving backward is a running theme throughout the novel. The past is in some ways seen as barbaric and retrograde here (people are literally riding in covered wagons at the end). But it isn't all urban decay and a lack of electricity and the Oregon Trail. The past is also a key part of Galt's values and the idea of Atlantis. Through Atlantis, Galt wants to resurrect the idea of a lost golden age, as represented by figures like Nat Taggart and childhood values like confidence, optimism, joy, and self-centeredness.
Over the course of the novel, Dagny and Hank both learn to accept and value their pasts rather than ignore them, demonstrating the importance of personal history.
Galt argues that his fight is centuries old, but it is actually more a product of the industrial age.