depending on your fare bucket, it’s not likely that you would get a full refund when you cancel. I once had such an issue. I included the wrong last name. I’ve called immediately the call center and they’ve directed me to the back office. The back office called me, told me to buy exactly the same flights again, call them back, and they would refund the full amount for the first ticket. I did as instructed, and they did refund me the full amount. Of course what happened to me is not any policy or anything, and it was just a good will action. TK did not have to refund me.
in your case, the difference is that you’ve cancelled without contacting them. I would say your chances are slim. At this moment, the best course of action would be to use the feedback form as the phone agents cannot do anything about your canceled ticket at the moment. Disputing with your bank would not help because TK should have all the legitimate documents to show that you indeed bought the ticket and you accepted all the cancellation charges.
in short, it will all depend on TK’s goodwill.