Objection 1. It would seem that satisfaction is neither a virtue nor an act of virtue. For every act of virtue is meritorious; whereas, seemingly, satisfaction is not, since merit is gratuitous, while satisfaction answers to a debt. Therefore satisfaction is not an act of virtue.
Objection 2. Further, every act of virtue is voluntary. But sometimes a man has to make satisfaction for something against his will, as when anyone is punished by the judge for an offense against another. Therefore satisfaction is not an act of virtue.
Objection 3. Further, according to the Philosopher (Ethic. viii, 13): "Choice holds the chief place in moral virtue." But satisfaction is not an act of choice but regards chiefly external works. Therefore it is not an act of virtue.
On the contrary, Satisfaction belongs to penance. Now penance is a virtue. Therefore satisfaction is also an act of virtue.
Further, none but an act of virtue has the effect of blotting out sin, for one contrary is destroyed by the other. Now satisfaction destroys sin altogether. Therefore it is an act of virtue.
I answer that, An act is said to be the act of a virtue in two ways. First, materially; and thus any act which implies no malice, or defect of a due circumstance, may be called an act of virtue, because virtue can make use of any such act for its end, e.g. to walk, to speak, and so forth. Secondly, an act is said to belong to a virtue formally, because its very name implies the form and nature of virtue; thus to suffer courageously is an act of courage. Now the formal element in every moral virtue is the observance of a mean. wherefore every act that implies the observance of a mean is formally an act of virtue. And since equality is the mean implied in the name of satisfaction (for a thing is said to be satisfied by reason of an equal proportion to something), it is evident that satisfaction also is formally an act of virtue.
Reply to Objection 1. Although to make satisfaction is due in itself, yet, in so far as the deed is done voluntarily by the one who offers satisfaction, it becomes something gratuitous on the part of the agent, so that he makes a virtue of necessity. For debt diminishes merit through being necessary and consequently against the will, so that if the will consent to the necessity, the element of merit is not forfeited.
Reply to Objection 2. An act of virtue demands voluntariness not in the patient but in the agent, for it is his act. Consequently since he on whom the judge wreaks vengeance is the patient and not the agent as regards satisfaction, it follows that satisfaction should be voluntary not in him but in the judge as agent.
Reply to Objection 3. The chief element of virtue can be understood in two ways. First, as being the chief element of virtue as virtue, and thus the chief element of virtue denotes whatever belongs to the nature of virtue or is most akin thereto; thus choice and other internal acts hold the chief place in virtue. Secondly, the chief element of virtue may be taken as denoting that which holds the first place in such and such a virtue; and then the first place belongs to that which gives its determination. Now the interior act, in certain virtues, is determined by some external act, since choice, which is common to all virtues, becomes proper to such and such a virtue through being directed to such and such an act. Thus it is that external acts hold the chief place in certain virtues; and this is the case with satisfaction.
Source: Summa Theologica (New Advent)