A quick note to save someone else the 20 minutes I spent looking into this: there is a regulatory protein complex called CCR4-NOT that degrades poly-A tails on mRNA. The name CCR4 here stands for carbon catabolite repression 4, and is named after the protein in yeast.

This has nothing to do with the human immune protein named CCR4, which stands for C-C motif chemokine receptor 4, and is expressed primarily by T-regulatory cells.

In humans the homologous version of the yeast protein is called CNOT6 (per table 1 in this paper), for CCR4-NOT complex 6.

Hope that clears things up for another poor soul wondering how an immune specific protein could be generally implicated in mRNA degradation.