She has begged: "End the rift with Dad"
Samantha is worried that this could be their father's last Christmas and she's anxius that the pair may never talk again.
And he has been suffering from heart related issues which have concerned his family.
In the card, decorated with birds and holly, she tells the former Suits actress: "Holidays are a time for family and are sentimental.
"Dad has been trying to contact you and is very hurt because you are avoiding him.
"Life is short and you know Dad is wonderful. Please give him joy in his last years by showing you love him. The time is now."
Samantha, 54, who lives in the southern US state of Virginia, told The Sunday Mirror newspaper: "Dad could die before next Christmas."
"I'm hoping that won't be the case, but it would be tragic and sad if he doesn't get to be around to resolve this.
"I think Meg would harbour a lot of regret if this were his last Christmas alive and she didn't reach out and make things right.
"There is not another day or week guaranteed, so Meg needs to act quickly. The clock is ticking."
Pregnant Meghan is all set to enjoy a lavish Christmas at Sandringham House with Prince Harry and the rest of the Royal family.
Meanwhile, Thomas will be at his modest home in Mexico struggling with his health issues.
Samantha, who is Thomas' daughter by his first wife Roslyn, said: "Dad has always been big about Christmas, especially when we were growing up.
"We would spend it as one big family unwrapping gifts, getting our hands in the pie dough, cooking the dinner together and watching Christmas shows on TV. Meg loved that stuff.
"I love my sister but I don't agree with the way she's behaving. She needs to reach out and have a peaceful loving heart and say, 'We're a family, let's move forward and make this right'.
"You can't be a humanitarian on the world stage if you can't be a humanitarian in your own family.
"We all looked up to him (Prince Harry) but he doesn't seem to care anything about this family.
"Whether you're royal or not, you married into our family too and nobody is above being decent."
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