The 74-year-old Emmy Award-winner, who claims he raised Meghan, has been described as "toxic" by one royal expert.
"In my view, I feel her family have tried to cash in," says Victoria Arbiter of Thomas, a former Hollywood lighting technician who now lives in Mexico.
“They have sold her out, no matter the cost, they have proven that they can’t keep a secret and they are something of a liability," she explained to The Express, of the years that followed the announcement of Harry and Meghan's romance, which was plagued by tell-alls by Thomas, her much-older half-sister Samantha and half brother, Thomas Markle Jr.
"So there has been a lot of talk and commentary about how now that Meghan is a mother she should allow her father, Thomas Markle, to meet the baby.
"Yes, in a perfect world it would be wonderful for the baby of Sussex to have a hands-on grandfather.
"And of course a grandfather should have the opportunity to meet their grandchild but I don’t think we are dealing with a regular father here."
WATCH: THOMAS SPEAKS OUT AFTER SHOCKING LETTER