They later presented a trophy to jockey Frankie Dettori who won the St James's Palace Stakes on Without Parole.
"The palace was given no heads up on Thomas' interview", the source said.
Nevertheless Meghan was cheered as she joined the Queen for one of the monarch's favourite events. "It's a sad state of affairs".
"Well of course it's "wow", it comes out as a "wow" but you know this is my daughter".
"He said, 'Hello Thomas.' I said, 'Hi Harry.' It became a conversation back and forth, mostly about politics".
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Ahead of the wedding, it was revealed that Thomas had staged paparazzi photos of himself preparing for his trip across the pond, though he was unable to make the nuptials due to the fact that he underwent heart surgery just a few days before his daughter got married.
He added that Meghan and Harry wanted him to walk her down the aisle "from the very start" and noted that Harry had given him advice on how to handle the encroaching press.
In another conversation, he said, he was complaining about not liking US President Donald Trump and Prince Harry responded by saying "give Donald Trump a chance". And I said, 'You're a gentleman.
The 73-year-old spoke about a phone call that took place between him and his new son-in-law, Prince Harry, whom he has never met face-to-face.
Prince Harry's press office declined to comment on the televised interview, which could raise eyebrows because senior Royal figures are scrupulously careful not to comment publicly on domestic or global political affairs.
Markle also claimed that he discussed politics with his new royal son-in-law, including the United States president and Brexit. In this interview, he apologized for doing so, admitted it was a mistake, and explained that he was simply trying to change his image - not make money.
It's just further proof that good hats run in the royal family.
"It was nearly a 30 minute interview - unheard off for members of the family", the source told Radar.
He also expressed the hope that he had not offended Meghan and Harry by giving the interview.