No Recovery Phrase

I recently purchased some ATOM on the Bilaxy exchange. I went to transfer it to Binance but didn’t include a memo tag and all of it got stuck in limbo. Binance was able to locate it and reverse the transaction but it all got sent to the Cosmo address to which I was never given a recovery phrase for it because it was purchased on Bilaxy. What do I do to gain access to my ATOM?

I don’t think you can get a recovery phrase to an exchange wallet, or I misunderstood the question