Rowling stated in a webchat that Hermione found her parents in Australia and relieved them of the memory charm she had placed on them. They agreed that the Time-Turner should be destroyed and Hermione hid it away. Nineteen years after Voldemort's death, Hermione and Ron Weasley are married.
FOR: Harry and Hermione always had far fewer arguments than Hermione and Ron
That's how it was conceived, really. Ron is angry because he feels Crookshanks is responsible for Scabbers' disappearance, while Hermione fiercely maintains that Crookshanks is innocent. Let us know in the comments!