The cloth is called a humeral veil. “The subdeacon stands behind the deacon while the celebrant sings Dominus vobiscum and Oremus at the offertory. He bows at the word Oremus, then genuflects and goes to the credence table. Here he receives the humeral veil on his shoulders from the M.C. [With the humeral veil he carries the chalice etc. to the altar.] He takes the chalice veil from the chalice; then he holds the chalice at its knob in the left hand bare (not through the humeral veil).…”
Now you know.