The correct answer is B. put on a show of.
To feign something means to fake it, to pretend that you are something you are actually not. Sir Gawain did this when he was supposed to fight the Green Knight - he was pretending to be brave and unaffected by the Green Knight when in fact he was really scared of fighting him. Not only was he scared of the Knight, but also of dishonoring his lord by losing the battle.