Jonathon Karl should be banned from any further briefings. He and the rest of the hacks aren’t interested in gathering information of facts. They are there to promote their, and their network’s (or newspaper’s) agenda to get Trump.
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Karl is the current President of the White House Correspondents’ Association. He is the one who decides which reporters get to be in the room for any and all of the pressers.
So he ain’t gonna get kicked out anytime soon.
Then Trump should just ignore him.
All President Trump has to do is tell his people to not let him in the interview room. This WHC thing has no governmental standing and the Presidency controls who can come and go whoever on the WH grounds and buildings period.