Call THY and make the reservation. Ticket will have to be issued by your local ticket office though.
Fore sure there will be add. YQ (fuel charges) when your book TLV-IST-JFK rather than IST-JFK. Look up the itinerary on ITA Matrix to get a picture of the YQ, taxes, surcharges to be paid if you book a (revenue) ticket TLV-IST-JFK with TK