When I read about the Fourth Crusades' attack on Constantinople, I have an idea of how Rome was responding: first the excommunication of the crusaders, then gradual accommodation to the idea of Latin rule over the former Byzantine territories. As Nicaean Empire regained control over their territories, Rome was trying to negotiate the unification of the Eastern and Western churches, but was keeping the idea of a crusade (Charles of Anjou's plan) as a threat if the reunification didn't work.
I don't know anything about how the Northern Crusades worked as far as Rome's attitude, though. How did they view the fact that the Teutonic Knights had gone outside of their mission of subduing the Baltic pagans to attack Orthodox Christians? Did Rome attempt to negotiate some sort of "if you come into communion with Rome, we'll tell the Teutonic Knights to knock it off under threat of excommunication" ultimatum? By this point, had they come to regard the invasion of Orthodox states as no more problematic than the invasion of Pagan states, since it was about a generation after the Fourth Crusade?
I came across this in a search. The TO had their own power base, financial resources, and economy. Essentially they were an army with a state. I would even argue that they resembled the early Prussian army. There was little the Pope could do to control them, and they were so far north fighting enemies that matter little to the rest of Europe, so they were largely allowed to do as they pleased.