Yes, it shows at the least that there were great differences about tactics.
“”Allied diplomats pressed Pope Pius to be silent on Nazi deportations’
“U.S. and British diplomats discussed exerting pressure on Pope Pius XII to be silent about the Nazi deportations of Hungarian Jews, according to newly discovered documentation. The British feared that the wartime pope might make a “radio appeal on behalf of the Jews in Hungary” and that in the course of his broadcast would “also criticize what the Russians are doing in occupied territory.” Sir Francis D’Arcy Osborne, the British ambassador to the Vatican, told an American diplomat that “something should be done to prevail upon the pope not to do this as it will have very serious political repercussions.”...””
“Was Pius XII ‘Hitler’s Pope’?”
“Pius XII: the legends and the truth”
That would be in the spring of 1944, by which time the war was approaching it's greatest battles, and nearly all the Jews doomed to die were already dead.
From remarks quoted in post #7 above, it appears that as of autumn 1942, British Ambassador Osborn was trying unsuccessfully to convince Pope Pius XII to publicly condemn the Holocaust.