Source : Webster's Revised Unabridged Dictionary (1913)

Conscience \Con"science\, n. [F. conscience, fr. L. conscientia,
   fr. consciens, p. pr. of conscire to know, to be conscious;
   con- + scire to know. See {Science}.]
   1. Knowledge of one's own thoughts or actions; consciousness.
      [Obs.]

            The sweetest cordial we receive, at last, Is
            conscience of our virtuous actions past. --Denham.

   2. The faculty, power, or inward principle which decides as
      to the character of one's own actions, purposes, and
      affections, warning against and condemning that which is
      wrong, and approving and prompting to that which is right;
      the moral faculty passing judgment on one's self; the
      moral sense.

            My conscience hath a thousand several tongues, And
            every tongue brings in a several tale, And every
            tale condemns me for a villain.       --Shak.

            As science means knowledge, conscience
            etymologically means self-knowledge . . . But the
            English word implies a moral standard of action in
            the mind as well as a consciousness of our own
            actions. . . . Conscience is the reason, employed
            about questions of right and wrong, and accompanied
            with the sentiments of approbation and condemnation.
                                                  --Whewell.

   3. The estimate or determination of conscience; conviction or
      right or duty.

            Conscience supposes the existence of some such
            [i.e., moral] faculty, and properly signifies our
            consciousness of having acted agreeably or contrary
            to its directions.                    --Adam Smith.

   4. Tenderness of feeling; pity. [Obs.] --Chaucer.

   {Conscience clause}, a clause in a general law exempting
      persons whose religious scruples forbid compliance
      therewith, -- as from taking judicial oaths, rendering
      military service, etc.

   {Conscience money}, stolen or wrongfully acquired money that
      is voluntarily restored to the rightful possessor. Such
      money paid into the United States treasury by unknown
      debtors is called the Conscience fund.

   {Court of Conscience}, a court established for the recovery
      of small debts, in London and other trading cities and
      districts. [Eng.] --Blackstone.

   {In conscience}, {In all conscience}, in deference or
      obedience to conscience or reason; in reason; reasonably.
      ``This is enough in conscience.'' --Howell. ``Half a dozen
      fools are, in all conscience, as many as you should
      require.'' --Swift.

   {To make conscience of}, {To make a matter of conscience}, to
      act according to the dictates of conscience concerning
      (any matter), or to scruple to act contrary to its
      dictates.

Source : WordNet®

conscience money
     n : payment made voluntarily to reduce guilt over dishonest
         dealings