Ok, maybe he can’t be barred from the White House. However, I’m sure he can be pulled aside by the Secret Service for “additional screening” right before the press conference begins.
And during his live shots the background should be trucks blocking the view of the white house. I’m sure the fire/police could stop by, with sirens set to extra loud. Of course the white house must have lawn sprinklers that require constant adjustment, not to mention the lawn must be mowed quite often. Then there’s those darn noisy helicopters. And intruder alert drills.