Possible Jewish ancestry in Italians isn't that surprising. Jews are ultimately Mediterranean/Middle Eastern in origin and, since Ashkenazi European Jews combine European ancestry with the original Mediterranean/Middle Eastern ancestry of the Hebrews/Israelites, this produces a tendency to cluster with Southern European populations a lot of times, like southern Italian and Greeks, themselves a blend of various European and Mediterranean populations.

What I'm saying is that trace Jewish DNA results might simply be "noise" and an attempt to classify your Mediterranean and/or West Asian DNA as something more specific when it may not be specifically of Jewish origin. I have trace European Jewish DNA results myself. My immediate ancestry is Sicilian/Italian, Anglo-Irish, and Alsatian (French-German border region). I suspect that this trace Jewish ancestry is either part of my Sicilian/Italian heritage (Mediterranean) or perhaps it could also be part of my Alsatian ancestry (many Ashkenazi Jews historically lived in the French-German border region).