Your badbank change is linked to your premix coinjoin transaction. So, if you spend the badbank, the receiver of the badbank sats can see whatever premix tx that is linked to the badbank sats being spent.

Further mixes in postmix can cut the link from badbank sats to the postmix sats, but whoever received those badbank sats can still tell how much coin was involved in the premix tx. As such, you should really not spend your badbank sats, especially not send it directly to a third party.

What I usually do with my badbank change is that if it's a big enough utxo, I'll do another mix of the badbank utxo into a smaller pool. I'll mix it until it's too small to mix, then I'll just leave it in the badbank account. But beware to never mix 1 bandbank utxo with another badbank utxo, because by doing so, you're linking 2 or more separate coinjoin transactions together. If you're going to mix badbank change, do them 1 by 1.