I think it's more likely Harry than Charles S giving a V to the Royal Family.
I'd have thought Meghan would jump at the chance to stay at Althorp and capitalise on contact with Diana's relatives, establishing the historic connections of her little Prince and Princess.
It's probably just idle gossip anyway, as pp said, every Christmas there's a "will they/won't they" go to Sandringham which is never going to happen, but now there's a new angle.
However if there really is an invitation and they did go then it will be very difficult for King Charles - it would look very churlish if his Grandchildren he has barely seen would be staying a mere 2 hour drive away over Christmas and not make an effort to see them. And indeed he may wish to see them, as a Grandfather. But from the point of view of the monarchy, and managing H&M, there will surely be a reluctance to give them any chance to capitalise on Royal contact, or to worm their way back into the fold.
A simple invite to afternoon tea on Boxing Day is anything but simple. W&C could easily absent themselves, staying at Anmer, perhaps with guests from the Middleton family. What of the other Royals - would they stay out extra long on the Boxing Day shoot and leave C&C to it? Or if they have to make a show of manners and stay, children included, well then, H&M are right back in there.
Then there is the issue of privacy and security. Would the invitation come with a warning that no mobile phones allowed? How to police that politely? Get security to check them over?????
A condition that there would be no photography except by a palace approved person? Camilla ❌, random footman❌, Johnny in his kilt ✅
Photos shared strictly for private family mementos only? What will the palace do when the photos make their way into the public sphere - maybe accidentally left in prime position on Meghan's desk at the next photo shoot "Oh, so sorry I forgot".
In the unlikely event they tried to impose a NDA (or an informal privacy agreement) on all conversations and details of the occasion, and in the unlikely event H&M agreed, what could the palace do when the NDA was ignored and all the details found their way into People magazine via five friends - "Oh so sorry, I was just chatting with my friends, I had no idea they would be so naughty and sell the story to People magazine".
There's just no way to control them.
It would definitely be a heads you lose, tails you lose situation for the King, with H&M able to sell at least a chapter of whinge whatever way the coin fell.