Objection 1. It would seem that restitution is not an act of commutative justice. For justice regards the notion of what is due. Now one may restore, even as one may give, that which is not due. Therefore restitution is not the act of any part of justice.
Objection 2. Further, that which has passed away and is no more cannot be restored. Now justice and injustice are about certain actions and passions, which are unenduring and transitory. Therefore restitution would not seem to be the act of a part of justice.
Objection 3. Further, restitution is repayment of something taken away. Now something may be taken away from a man not only in commutation, but also in distribution, as when, in distributing, one gives a man less than his due. Therefore restitution is not more an act of commutative than of distributive justice.
On the contrary, Restitution is opposed to taking away. Now it is an act of commutative injustice to take away what belongs to another. Therefore to restore it is an act of that justice which directs commutations.
I answer that, To restore is seemingly the same as to reinstate a person in the possession or dominion of his thing, so that in restitution we consider the equality of justice attending the payment of one thing for another, and this belongs to commutative justice. Hence restitution is an act of commutative justice, occasioned by one person having what belongs to another, either with his consent, for instance on loan or deposit, or against his will, as in robbery or theft.
Reply to Objection 1. That which is not due to another is not his properly speaking, although it may have been his at some time: wherefore it is a mere gift rather than a restitution, when anyone renders to another what is not due to him. It is however somewhat like a restitution, since the thing itself is materially the same; yet it is not the same in respect of the formal aspect of justice, which considers that thing as belonging to this particular man: and so it is not restitution properly so called.
Reply to Objection 2. In so far as the word restitution denotes something done over again, it implies identity of object. Hence it would seem originally to have applied chiefly to external things, which can pass from one person to another, since they remain the same both substantially and in respect of the right of dominion. But, even as the term "commutation" has passed from such like things to those actions and passions which confer reverence or injury, harm or profit on another person, so too the term "restitution" is applied, to things which though they be transitory in reality, yet remain in their effect; whether this touch his body, as when the body is hurt by being struck, or his reputation, as when a man remains defamed or dishonored by injurious words.
Reply to Objection 3. Compensation is made by the distributor to the man to whom less was given than his due, by comparison of thing with thing, when the latter receives so much the more according as he received less than his due: and consequently it pertains to commutative justice.
Source: Summa Theologica (New Advent)