The necklace displayed at the Smithsonian is not the real Titanic artifact—it's a prop from James Cameron's 1997 film Titanic.
It's part of a "Hollywood Myth and Magic" exhibit showcasing iconic movie objects. While fictional, its intricate design and cinematic role make it a popular cultural artifact.
The real Hope Diamond (often conflated) is also at the Smithsonian, but in the gem collection.