I didn't see this, but I read a bunch of stuff in the t.v. guide & I can't remember it all. What I do remember is...
The suite that the players stay in is not a real suite -- it was constructed for the show. Also, the suite & the boardroom are on the same floor -- so Trump just says, "go back up to the suite" for effect.
The players bags are never fully packed - I think there are a few items in there when they roll them down, but if they're fired, people who work on the show go back up & get the rest.
The taxi that the "losers" catch when they leave takes them a couple of blocks over to another hotel where all of the other "losers" stay for the remainder of the show.
There's more, but I forget...