So this wasn’t during a competition round, but what would your ruling be if you witnessed this happening? (Just Jack’s putt – don’t worry about the banter with Johnny Miller before or the fact that he had just popped the ball down on the green).
You will notice that Jack’s caddie ran over to take the flagstick out when he saw it might go in. He wasn’t close to the hole when Jack hit the putt and hadn’t been asked to attend the flagstick.
Rule 13.2b(1) defines when a player has authorised the flagstick to be attended as follows:

And 13.2a(3) stops you or your caddie removing the flagstick if you have decided to leave it in the hole.

So if this were a competition round Jack would get the general penalty – loss of hole in matchplay or 2 strokes in stroke play.