Just write off the ticket - TK will not touch it. In the future, I recommend booking directly with TK.
I had a similar situation in December, except it was a $8000 of tickets for my family of 4. Talking with TK Elite Plus desk and the Agent both went nowhere, and the only way we managed to get a refund is by VDBing and then waiving compensation. It's unlikely that you'd be able to pull off a similar stunt, and for the price of an error fare it's not worth it anyway.