The court presided by Judge Lewis Kaplan was hearing on a motion by the royal's lawyers to dismiss the civil case against him.
Meghan and the Queen travelled together to Chester on the Royal Train in June 2018.
The Duke of Cambridge faces a "poignant" reminder about his mother when the Duchess of Cambridge becomes Princess of Wales.
Jordan revealed that she believes Giuffre's claims about the Duke of York because of her own run-ins with him.