Following the death of Queen Elizabeth II, Prince Harry and Meghan Markle's children are now technically Prince Archie and Princess Lilibet.
Traditionally, the change in title is an automatic right with ascension of a new monarch. In 1917, King George V had established new rules that granted the children and grandchildren of a sovereign to be automatically entitled to the title His Royal Highness and prince or princess. (At the time of their births, Archie and Lilibet were the great-grandchildren of a sovereign.)
It is possible that King Charles could still revoke those titles from his grandchildren.
In an interview with Oprah Winfrey last year, Meghan had said that the royal family discussed changing the protocol in order to keep Archie from acquiring the title of prince. She also said that, while she was pregnant with Archie, the family decided to not grant him the HRH and prince title, connecting their decision to concerns over "how dark" the baby's skin would be.
"In those months, when I was pregnant, all around this same time, we had in tandem the conversation of he won't be given security, he won't be given a title... and also concerns and conversations about how dark his skin will be when he's born," Meghan told Winfrey at the time. "That was relayed to me from Harry, that was from conversations that family had with him. It was really hard to see those as compartmentalized conversations."
In order to remove Archie and Lilibet's new titles, the king would have to issue a Letters Patent amending their rights, per The Guardian.