To answer the question - "Why would you do that? What made you think that Bitmex deals in USDT?" - I didn't realize that I WAS doing that.  It was a mistake.  I took the money out of Bittrex while it was in a BTC/USDT trade. Yes - a bonehead move, now I know.  The reason my mind was thinking that was because the only way to transfer BTC from GDAX is to put it into a trade and then siphon off some of the trade to send to another exchange.  So, that process was in my mind.  Yes, hindsight is always more illuminating than foresight.   I assumed that the funds coming out of the BTC/USDT on bittrex would have ended up on Bitmex as BTC.  Now I know!  I learned a painful lesson.  Hope that answers your question.

Here is the response I got from Bitmex:

That is not possible. It is a multisignature address and the private keys are held in offline devices and not accessible.

And, this is what it says on the Bitmex Deposit page:  Any unsupported coins sent here will be lost.

I was in a hurry and didn't read it completely.  But, aside from that, I did not realize that I was sending USDT.

So there is no recourse for me?

Thank you.  I will check that out.

I sent several hundred dollars in USDT from my Bittrex account to Bitmex. The transfer did not go through. Bitmex says to contact Bittrex. Bittrex says they can't help.

Here is what I got from Bittrex: "Unfortunately this is outside our realm of support, you will need to research how to remove a private key from a XBT address and import it into a USDT wallet to recover these coins. You will need to do the research as we can no longer be of any further assistance on this issue."

I have no idea on how to proceed from here.   Has anyone ever dealt with this issue? How do I proceed to getting this resolved?

Am I supposed to ask Bitmex to remove the private key?  If they agree to do that, then what is the next step?