By "airport taxi duration" TK most likely means the time spent in BKK taxing the aircraft from gate or remote stand (at BKK they were taken by bus to the aircraft?) to the runway take off position (which was only 15 min so not excessive) or taxing to the gate after landing at IST (I can't see how long that took). The aircraft didn't leave BKK late/there was no delay in BKK. As I explained to you the real reason for the delay was the 11h15min flight time (in the air) because of a longer more southernly flight path.

No, I don't think you are eligible for some compensation (or "credit" - TK don't give credits/refunds). Maybe you can get some M&S Miles if you push.

I think you should reply back maintaining that your parents are eligible for compensation due to delay because the flight time was 45min longer than usual due to the longer route chosen. If TK still refuse, I suggest to move on/forget it.