The Duchess of Cambridge captured her son on the bonnet of a Land Rover, his great-grandfather's favourite car.
Another remark about Prince Philip was also cut from the UK broadcast.
The Duke of Edinburgh was laid to rest last weekend, but some viewers were not happy with how much airtime the BBC dedicated to the event.
The Queen issued the statement on her 95th birthday, thanking the public for providing comfort during "a period of great sadness".
The Duchess of Sussex was unable to attend the ceremony, as she is pregnant and was advised not to travel.
Sophie, the Countess of Wessex, took the picture in the Scottish Highlands in 2003.
More than 100,000 people filed official complaints to the BBC about their response to the Duke of Edinburgh's death.
The Duke of Edinburgh’s funeral is due to take place on Saturday 17 April.
Following the Duke of Edinburgh's death the BBC wiped its schedules across both BBC One and BBC Two.
The service's website was given a redesign that left visually-impaired passengers unable to book trips.