Problem with BTT, got confused between BTT and BTT Old

Hi, I think I made a mistake. I got confused between the old BTT and the BTT TRC20. I sent about 67$ BTT from coinex to my binance account. The tronscan says the transaction has been confirmed, but after a few days nothing appeared so I submitted an application for retrieval of funds, and here is what binance support said: "the BTT you deposited is different from the one we support (BTTOLD), so please provide a TRX network address and we'll try to help to return." I need to pay a 0.001 BTC fee (roughly 47$) to do the refund. Newbie questions: If I just wait for binance to allow for BTT(new), will my coins magically appear in that new wallet? If I decide to move forward with the refund application, Will the 0.001BTC processing fee be withdrawn even if they cannot retrieve the coins? Thanks.