There are no records for people leaving the US.
It was not uncommon for men to travel back and forth between the US and Italy--they came here for the work and quite often would get established before sending for the rest of the family (or they would bring the money back to Italy).
My great grandfather traveled back and fourth 4 times, twice with his wife and twice without her. On one of their trips back to Italy my great grandmother became pregnant with my grandfather. She and her husband traveled to the US while she was pregnant (1901), and my grandfather was born in NYC a few months after their arrival.
All three later returned to Italy. My great grandfather came back to NY alone the next year (1916) but died shortly after his arrival. I don't know if his wife and son had planned to join him in NY at a later date or if he planned on returning to Italy.
My grandfather, now in Italy with his widowed mother, wed my grandmother there in 1922. My father was born in Italy in 1923. In June 1924, my grandfather came to the US by himself. My father and my grandmother, who was now pregnant with her second child, arrived in NY in Nov 1924. As far as I know, that's the last trip any of them made.