If there was an error in the Letter of Invitation I don't see any basis for claiming IDB or complaining to DOT. The fact is that it is the responsibility of pax to produce the necessary and correct documents needed for immigration. TK was not in a position to let her travel to ASB, nor to IST when the the final destination was ASB (and certainly not based on a promise that the issue would be fixed before landing at IST; what if it wasn't fixed?). For sure this being an award also complicated matters. I don't see any duty on TK to amend the award ticket to IST only because pax is ineligible to enter the country of final destination. Sorry, it may seem a bit harsh, but I think you are barking up the wrong tree here.

Ask for refund and book a new award or revenue ticket for your wife.