Will be traveling to Italy on Delta with one way ticket to Rome from jfk. Then 13 day tour ending in Palermo Sicily. Delta had poor choice of flight in Palermo and they were operated by Ita. So I booked return to jfk on Ita. Question is will I have problem leaving JFK because of one way ticket

JFK is not going to care. Italy might, though at passport control. They may ask when your return flight is, and you tell them. Or they may not.

They don't care HOW it is booked such as one way in both directions, round trip or multicity flights. They just care that it is booked and you're intending to return home on it. But again, the US doesn't care about the HOW either.

Thanks for info. I don’t think Italy customs will be a problem because I can show tour documents and ITA return e-ticket. My concern is with delta at jfk questioning my 1way ticket

Why would an airline care?

Especially since you paid a lot for that one-way ticket.

Airlines care because if the OP gets bounced the airline gets fined and has to fly them back.

I don't understand why the OP didn't book a R/T. They booked a one way with ITA to avoid a flight operated by ITA?

I'll admit an American isn't likely to get hassled by immigration

https://www.iata.org/en/publications...act-on-travel/

Thing is, that can happen regardless of how a traveler purchases the tickets.

The OP made this decision. Regardless of reasons why, they still have valid tickets, just not purchased in a way that an airline may prefer.

Which is what the OP asked about. Will the airline be unhappy?

I booked Delta out of jfk to Rome on miles. Saved a lot. However, Delta doesn’t have flights out of Palermo. They have one code share flight at 6am on ITA to Rome then connect to delta there. That’s too early. ITA had many choices out of Palermo connecting in Rome to Ita flight to jfk. That made more sense to me

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My last trip, I booked different airlines through reward travel. Two one way tickets using two different systems.. Nobody cared and I can't imagine they would,

The airlines will, of course, check your passport. Just make sure you have at least 3 months left on it from your planned exit from the EU. Sometime next year the ETIAS travel authoritization will be launched.