Slightly over 50,000 Italians were held in American POW camps during the war - plus several hundred thousand more in North Africa, Britain, and so on, and continued to be held even after the capitulation of Italy. From 1943 onward, there was some effort made to improve the conditions of the camps where Italian POWs were held, but most would remain in captivity for the remainder of the war.

The US had a pretty pragmatic reason for this, as POWs provided free labor, freeing up American men from jobs to instead fight. Italian POWs provided in excess of 10 million man hours of work during the war! To be sure, the Americans at least made the offer to Italy in '43, but on essentially impossible terms. The agreement negotiated was that the Allies would free Italian POWs they held once Italy freed Allied POWs it held. But those were mostly on the mainland, and mostly in camps that fell into German hands when Italy surrendered and Germany, for some strange reason, didn't decide "OK, we'll leave then I guess". The US might not have said to Italian officials' faces, but there was no secret why they made such impossible demands. A 1945 report noted “We felt it absolutely necessary from the military standpoint to keep these people [i.e., Italian prisoners] and get useful labor out of them".

Source: Life and Death in Captivity: The Abuse of Prisoners During War by Geoffrey Wallace