let my try to explain it more succinctly what i'm trying to accomplish waxwing (npub1vad…nuu7)!
the first DLEQ proves C' = k*B'
second DLEQ proves C = k*Y
it Alice gives Carol the first DLEQ Crol can't produce or verify C from it without r. r blinds the relationship between C' and C thus protects the 'unlinkability' aspect. Alice however can reveal the second DLEQ to anyone.