I recently flew from JFK to Tel AViv with a stop at Rome. Our flight from New York was delayed by 6 hours. They told us it's because the plane had to turn back to Rome because of a medical emergency. As a result, they also had to reschedule our connection flight from Rome to Tel Aviv.
We landed at Rome 20 minutes before the connection flight, but they refused to let us on board, saying they have already sold our tickets. They rescheduled our flight (again) to 8 hours later.
Eventually, instead of landing in Tel Aviv at 14:00pm, we landed at 03:00am.
Alitalia is refusing to compensate, claiming the airport at JFK caused the delay (which isn't what we were told at that day).
I live in Israel and they have offices here. What can I do? I don't want to use any website that takes 25% of the compensation.
Should I simply file a lawsuit?