If I were you, I'd consider changing my lawyers. This is explicitly forbidden by GDPR (art 28), you have to know what your contracted data processors are doing, and you have to have processes in place to assure data subjects rights (eg remove their data from your contracted third parties on request). Cookie banners have nothing to do with this, and you're in breach of GDPR cookie banner or not. If your lawyers didn't stop you from breaching art 28 but recommended slapping a cookie banner "to be extra careful", that's a major red flag.