You can't book a Tuesdays flight to IST (and get a free transfer hotel) when there are suitable flights LHR-IST the following day that fit the same IST-SCL flight better (i.e. has a shorter transfer time).

You can try to plead your case with the TK hotel desk staff, but if there is a later IST-LHR that would have made you ineligible for a transfer hotel (because of short transfer time) your chances are slim; I would say you have better chances playing the lottery in this situation.