not sure I understand the problem.
You deposited qtum token in to an ETH address? on another exchange?
If that's the case, then I think the receiving party still have your qtum. Qtum tokens are ERC 20 which means they are tokens on the ETH network.
So where ever you deposited should be at the receiving's exchange's wallet. Now whether they support qtum exchange or withdraw is a different matter. You will have to contact them and see.
It would be extra work on their part to get the token out for you. But I think they would be the only one that can do this for you.