Lots of people going on and on about TK being "fully responsible", etc. Yes, the OP needs to deal with TK rather than SK.

However, when you choose to credit miles to a partner programme instead of the operating carrier, the operating carrier needs to "pay" the ffp for those miles. A ffp isn't just randomly handing out miles like candy, they are getting paid for those miles. Behind the scenes, with netting off agreements, etc. But getting paid nonetheless.

If the operating airline isn't actually inclined to pay the partner ffp (it happens more than the "global seamless alliances" would have you believe), you end up with situations such as this one. Some, but not all, ffps still credit the miles in order to retain the goodwill of the member. TK, as we all know, isn't known for having empowered employees who can make such gestures.

From all that I can tell, SK are the ones playing games here, and TK employees aren't allowed to do anything about it.