E. Cobham Brewer 18101897. Dictionary of Phrase and Fable. 1898.
Though your sins be as scarlet, they shall be as white as snow (Isa. i. 18). The allusion is to the scarlet fillet tied round the head of the scapegoat. Though your sins be as scarlet as the fillet on the head of the goat to which the high priest has transferred the sins of the whole nation, yet shall they be forgiven and wiped out.