Game of Thrones editors wasted no time fixing their coffee cup mistake. Very quickly after the internet found the mistake, a producer apologized while expressing disbelief.
And they also quickly edited the scene so the slip-up didn’t haunt the legacy that Game of Thrones will have. I rewatched the scene and confirm the coffee cup IS gone.
In case you could forget the coffee cup:

And here is what it looks like today:

RIP Coffee Cup:

Entertainment Weekly reports that HBO has issued a acknowledged the removal: “HBO confirms the cup has now been digitally edited out of existence from Westeros on its streaming services. It exists now only in our memory. And in hundreds of screengrabs and memes.”
Never forget.