"I wanted to say a huge thank you to you for sending in the wonderful, very moving photograph of your grandparents," Kate said to Hayley.
"I'm so sorry for your loss. I'm hugely grateful for you sending in such a personal photograph," she added.
The image shows the couple embracing each other in their hospital beds - a heartbreaking scene that the Duchess described as "so moving", as the two passed away just days within each other.
"That's what I think is so lovely, is actually hearing people's stories, and the things that have really resonated for them."
The audio was published on the Cambridge's YouTube channel on Monday, where Kate and Hayley discussed the circumstances around the picture.
“I think things like that shouldn’t be taken for granted, particularly, you know, in the last few days of life," Kate said.
Hayley added: “Although obviously it’s a sad photo, it’s also so happy as well. When I look at it I feel really sad, but I also think, I feel really joyful, you know?"
More telephone calls between Kate and Hold Still participants are set to be released in the coming weeks on the Duke and Duchess of Cambridge's new YouTube channel.
The royal couple announced the launch of the channel on May 5 with a behind-the-scenes look at their life.
Kate released her book Hold Still just days later on May 7, and it includes images of key frontline workers and people isolated from family and friends.