Trivia: In the scene where Hagrid has dropped a "dead" Harry Potter, look quickly at George. He turns his head to the right and yells "Fred!" Fred has already been killed by Bellatrix Lestrange so it seems he may have forgotten this in a moment of grief.
Trivia: Jamie Waylett, who played Crabbe in previous movies, was unable to reprise his role due to being arrested for growing cannabis. Because of this, the filmmakers decided to kill off Goyle instead of Crabbe.
Chosen answer: Hermione knows this is an unusual request and she and (and Harry) suspect the bank knows that Bellatrix's wand was captured by Harry Potter (at the end of Part 1). Showing the bank manager the real wand would prove that this is not Bellatrix. The bank and Voldemort's minions expected that Harry and the others might go to Gringotts searching for a Horcrux in the Lestrange's vault. They are setting a trap for Harry and his accomplices.
raywest ★
Incidentally, if I remember right, in the book Hermione actually does hand over Bellatrix's wand, not realizing the Gringotts goblins already know the wand is no longer in her possession, forcing Harry to cast a timely Imperius Curse to avoid the entire plan being exposed.