What can I do?
If your transaction is under $5000, you can only hope Bittrex will at some point change their
cross chain recovery policy.
Public pressure may help, but ultimately it's the shitcoins that are to blame for using the same address format as Bitcoin. I can imagine exchanges creating an "annual cross chain recovery day", in which they handle all requests from the past year.
Technically, Bittrex can recover your Bitcoins but that would be at a security risk to them as they would have to import the private key for their usdt wallet into another Bitcoin wallet
This explains it nicely (it's about Kraken but Bittrex will use similar security measures):
This is what Kraken replied to me:
"You are absolutely correct about us possessing the private keys in this circumstance. That being said, it isn't as straight forward as you might think. Kraken is a cryptocurrency exchange and the nature of cryptocurrency exchanges are wholly different from the experience you might have with a personal wallet where you have easy access to the private keys. With things like the theft of Mt Gox, the internal compromise of Shapeshift, the social engineering of BitPay, and others, we must put security as the paramount concern. As such, our exchange is setup in such a way that nobody within Kraken can unilaterally move funds. We believe that this is a very important protection that makes it extremely difficult for client funds to be stolen by external or internal parties.
Only a very small group of people at Kraken (devs) have the ability to access your funds given an auditable thorough process of checks and balances. This makes the process extremely resource (time) intensive for the devs that have very full plates and very little time to dedicate to any specific task. They must prioritize all of our tasks internally and the requests of clients as best they can. We think that the prioritization of improving our UI/UX as to avoid these type of mistakes will show the greatest dividends for our clients.
For what it's worth, Kraken made an exception:
In this case we have decided that we are going to make an exception to our general policy of not recovering crypto tokens that have been sent to the wrong address and assist you with the recovery. However, our developers, who are required to recover the funds for you, are very busy at the moment.
We will have to ask you to wait a minimum of 90 days until the recovery can be attempted. These efforts will take time and may not be possible in some cases. We will give you an update only after the recovery has been completed. Please be patient as our team works to resolve your issue.