I suspect that Francis is using this to remind everyone who is still in charge.  At least I hope it is.  A little hardball politics against an odious figure like Burke is not a bad thing especially since Burke is definitely trying to force Pope Francis to resign.  

And yes Burke stepped in it by bringing up an old issues that the Knights had apparently resolved already and threatening Festing.  I suspect that he was threatening to have his buddies over at the Lepanto Institute publish this and Festing thought this would prevent bad press.  Of course, he has ended up getting more bad press.  And Burke gave Francis a convenient opening to move against him by dragging the pope into this.