There is still much we don't know about what happened at the K of M - it sounds like a political battle that got out of hand.  Such is the world today.  Discord, distrust are everywhere, even, evidently, within ancient religions and orders of chivalry.  

As for +Burke...  von Boeselager notes that Francis will appoint a papal delegate to take the role of spokesperson for the pope to the order.  Perhaps +Burke will continue as "spiritual patron" with a different definition of duties.  He could tour various sites where K of M actually operates, say Mass, actually see the people who are helped, bring a higher level face of the Church to those doing the good works and those suffering,  bring the cameras of world to record the need and the work being done.  He just would not advise on programs, agencies with which the KofM work, individuals hired or in leadership or membership in/of the KofM.    He just shouldn't have any authority.

Can Burke transform to a face of charity?