The Duke and Duchess also revealed that their three children, Prince George, Princess Charlotte, and Prince Louis, are missing their great-grandfather.
“They will all miss their much-loved grandfather and great-grandfather, but your message has provided great comfort at this difficult time," the card said.
The card included a picture of a smiling Philip in his military uniform.
William and Kate recently shared a series of images of themselves and their kids with Philip.
The Duke of Edinburgh passed away on April 9 aged 99, and in the days since, the family shared some incredible unknown memories of their father, grandfather and great-grandfather.
Kensington Palace shared two beautiful snaps on Instagram.
The first image shows William and Kate standing with the Queen and the Duke with their two eldest children, Charlotte and George while they visited Balmoral Castle.
In the other image, The Queen and Prince Philip are surrounded by their great-grandchildren - every single one of them at the time (later to join would be Prince Harry's son Archie, Zara Tindall's son Lucas, and Princess Eugenie's first son, August).
"Today we share, along with members of The Royal Family, photographs of the Duke of Edinburgh as a father, grandfather and great-grandfather," the caption read.
