I’m fascinated by the BWB and what role they will play in the series endgame. What happens if Tywin doesn’t send the obviously recognizable Mountain to do the raiding that causes their formation? Gregor’s stature is the final proof that Tywin is behind the attacks. Does Ned even form BWB with such an illustrious roster if he thinks the raiders are only regular knights under Tywin’s command? Certainly Loras doesn’t volunteer. Or is Tywin trying to draw out Ned with Gregor as the obvious clue?

Tywin is trying to draw out Ned. As as we learn in ASOS:

 "It was a trap, milady. Lord Tywin sent his Mountain across the Red Fork with fire and sword, hoping to draw your lord father. He planned for Lord Eddard to come west himself to deal with Gregor Clegane. If he had he would have been killed, or taken prisoner and traded for the Imp, who was your lady mother’s captive at the time. Only the Kingslayer never knew Lord Tywin’s plan, and when he heard about his brother’s capture he attacked your father in the streets of King’s Landing.“

Since the point is to draw out Ned, Tywin was always going to use Gregor. Now, if Ned hadn’t been injured he would have come himself, but Beric probably would have been called on to be part of the expedition, because he was a prominent lord in the royal court who had recently distinguished himself in the tourney, and who wasn’t associated with Loras Tyrell.