Thought an update might be useful...

I was concerned because there was no field to enter my KTN with my Turkish Airlines reservation/ticket, but I was able to use GE when entering the US on a recent flight. The Kiosk computer knew I was on the TK flight even without the KTN. Re-entry to the US to seconds. I called TK and asked and asked several TK employees, but nobody seemed to understand what I was asking, and I could not find a recent answer on FT or anywhere else, so I'm posting in case anyone has the same question.