I don’t know about the rest of the Italian stuff, but the pieces from Monte Cassino were saved through one of the few civilized acts of the Wehrmacht. Kesselring and the local commander Von Senger prompted and assisted the Augustinian monks in evacuating the art and archives of the abbey, as it was in the front line and at risk of destruction, and it was in fact destroyed. But much if not all its valuable contents were saved.
What part, if any, does the collection of religious art at The Cloisters have in all of this?