Address with a stolen private key

I have an address with Counterparty assets that has had its private key compromised. Whenever I try to send BTC to this address to allow me to move the assets to another address, some bot automatically transfers those bitcoins to another address. The good news is that whomever stole the private key to this address, does not know it has Counterparty assets as well. So I wanted to know, is it possible to use XCP instead of BTC to move these assets?

You can sweep that private key into a Counterwallet address and use a different address to make the BTC payment with!

How did this situation play out?