The portrait - which showed the royal couple in a photocall on the day of their engagement - originally replaced a portrait of the Queen's only daughter, Princess Anne and her husband Timothy Laurence in uniform.
However, now only a photo of Prince William and Kate Middleton and a photo of Prince William and Prince Harry wearing their uniforms remain.
According to Express, a source has criticised Her Majesty, suggesting that the House of Windsor was not prepared for the power of Harry and Meghan - who have "single-handedly modernised the monarchy."
The criticism follows the airing of ITV documentary Harry & Meghan: An African Journey, where the royal couple made several emotional confessions to broadcaster Tom Bradby (who has filmed three documentaries with Prince Harry).
The Duchess admitted she was struggling with royal duties and becoming a mother with the pressures of media scrutiny.
Tom asked Meghan about the "impact on your physical and mental health of all the pressure that you clearly feel under," to which she candidly replied:
"I would say - look, any woman, especially when they are pregnant, you are really vulnerable and so that was made really challenging.
And then when you have a newborn, you know?
"And especially as a woman it’s really, it’s really a lot."
The Duchess - who is a new mother to baby Archie Mountbatten-Windsor - continued: "Well, I guess, and also thank you for asking, but not many people have asked if I’m okay, but it’s a very real thing to be faint behind the scenes."
What's more, Prince Harry said he was afraid of "a repeat of the past," and is determined to protect his family from the same media scrutiny his late mother, Princess Diana, was subjected to.
The Duke also revealed that he had "good days" and "bad days" with his brother, Prince William, adding that they are "on different paths."
WATCH: Prince Harry confirms rift with Prince William in ITV documentary
An insider told the BBC that the Duke of Cambridge was worried Harry and Meghan were in a "fragile place."
Royal commentators believe the actions of Harry and Meghan have left the Queen and the more senior members of the royal family "very worried" about the direction the "divisive" couple are heading in.
Jonny Dymond, the BBC's royal correspondent, said: "I think they (the royal family) will be pretty horrified actually."