He said he could not attend the wedding because he was due to undergo heart surgery amid controversy he had staged photos to improve his image.
He has since made multiple TV appearances including Good Morning Britain (GMB) on which he has appealed to Meghan to “reach out” in order to “resolve any family problems”.
Ahead of Christmas Thomas has been pictured tidying his car outside his home in Rosarito, just across the Mexican border from San Diego, California.
Meghan’s sibling, Thomas Jr and Samantha, have urged her to end the apparent rift with her dad, who she last spoke to on the eve of her wedding.
Speaking to Piers Morgan on GMB earlier this month, Thomas claimed he sends text messages “every day” to Meghan and letters to Kensington Palace, where she lives with Harry.
“I’ve been ghosted”
He said: “I’ve been ghosted. I’m not sure why it’s happening. I love my daughter very much. I wish she would reach out, send me a text, anything. There has to be a place for me. I’m her father.”
In an earlier interview with GMB, Thomas said he “absolutely wanted” to walk Meghan, 36 down the aisle but chose to watch the ceremony from California, where he was recovering from heart surgery.
He added that had he not stayed in Mexico for the operation, thought to have been caused by stress, attending the wedding “would have killed me”.
He said he was “honoured” to let Charles take his place, but told Piers of his regret at missing “one of the greatest moments in history”.
“I can’t think of a better replacement than someone like Prince Charles,” he told GMB.