Really the carpet is not dirty it is damaged, nothing you do while removing it will make more damage.... at the very least you will clean out the poo and delaminates the carpet but this a better situation that having poo on the carpet.
They customers have a choice, they can have crap on the carpet or risk the cleaning slightly damaging the carpet. Who knows you might rinse it out with zero harm to the carpet.
But to answer your question, slowly rinse out the poo with a low psi hand tool but multiple passes