In Half Blood Prince, Dumbledore arrives at the Dursley's house to pick up Harry. Greeting Petunia, Dumbledore says "We have corresponded, of course."
Harry at that point thinks that Dumbledore is referring to the Howler sent by him to Petunia in Order of The Phoenix. But later in Deathly Hallows we come to know that Petunia had written to Dumbledore to accept her in Hogwarts. He of course was referring to that correspondence.
— Quora user Rishi Agarwal