Prince Harry appeared annoyed with his wife at one point in their new Netflix documentary when she joked about having to curtsey to the late Queen.
The Duke of Sussex recounted the conversation he had with Meghan when he first introduced her to Queen Elizabeth II, explaining that she would have to curtsy.
"How do you explain that you bow to your grandmother? And that you will need to curtsey? Especially to an American… that's weird," he said.
The Duchess said it was "surreal" and that she thought he was joking when he asked if she knew how to curtsey, then giggled as she performed an exaggerated curtsey for the camera.
"I was like, pleasure to meet you, Your Majesty. Like, was that OK? It was so intense," she said. "I didn't know what I was doing!"
Prince Harry shot her a look that suggested he was not sharing the joke.
One royal insider said: "The truth is, this is a real royal family, they're not playing a role.
"It's a real Queen and now a real King. Do the family bow to them? Yes, it's about respect. How did they not know that?"
Gyles Brandreth, the royal author, branded the Duchess of Sussex's demonstration of her curtsy as "mocking" and "embarrassing".
He told Vanessa Feltz's Drivetime show on TalkTV: "Nobody curtsies to the Queen like that, and nobody would have advised her to do it that way."
Brandreth, a friend of the royal family, said the King was unlikely to watch the docuseries as he does not spend much time tuning in to television, but that the show was "interesting" rather than "explosive".
He added of Harry: "He would know that the bow, as it were, is a brief nod and the curtsy is to show respect for the sovereign, and in the case of the Queen - a lady in her 90s who actually had earned respect through a lifetime of service, and that was it.
"To do this sort of mocking thing is uncomfortable, but it is a cultural difference. It's like you would do a curtsy if you were playing in Snow White."
Brandreth added that the trailer had been more exciting than the full programme so far.
"If you take the long view of history, you find it interesting, but you don't find it alarming. I don't think, for example, the King would have watched it," he said.
"He doesn't watch very much television. I don't think he would have learned very much except about the unhappiness of his son in the situation. We can all learn lessons about how we run things."