This is quite sad and disappointing but that's the truth of it only that exchange can help you and no body else. You made a mistake, before sending any coin you need to be sure of the network you are selecting most especially with many networks now which supports USDT, you ought to cross-check properly to be sure you are on the right one.
As said earlier the only people that will help is exmarket support, you have to contact them again and tell them you can pay a certain fee for their troubles, no one is above mistake though, mind your approach towards the issues and I hope they listen and help you out.
Yes it's possible to recover but might not be all though since the exchange might charge you, but it all falls on them to agree to help you.