Conscience Money,

Chambers's Encyclopaedia, Volume 3: Catarrh to Dion, p. 426

Conscience Money, money paid to relieve the conscience, is a not inapt term for money sent to the Chancellor of the Exchequer in payment of a tax that had previously been evaded, and in regard to which a tender conscience feels that something remained to be done. The conscience money is often sent anonymously.

Source scan(s): p. 0437