Restitution is only ever, even theoretically possible, in crimes involving possessions, eg, monetary debts, stolen property, damaged property, etc.
Restitution is NOT possible for a range of other offences such as, murder, sexual abuse (including rape), character assassination, public deprecation, physical abuse, etc, etc.
The passage in Matt 5:23 does not have any particular crime in mind - anything that prevents two people enjoying a complete friendship. Recall that the context of this verse is Jesus exposition of the moral law and its expansion under the new covenant. In particular, the section is an expansion about the generalized crime of murder (Matt 5:21-26). Within this law, Jesus included hatred, unjustifed anger, even calling someone a fool, etc.
Jesus encourages His followers to have nothing between them of any kind and that all their relationships should be characterized by love:
A new commandment I give you: Love one another. As I have loved you,
so you also must love one another. By this everyone will know that you
are My disciples, if you love one another.
On occasions, this may involve restitution, but that is not always possible or even practical. However, the important point is that such differences be resolved so that a full reconciliation is possible. Paul had a similar instruction in 2 Cor 5:18-21.
In commenting on Matt 5:23, Barnes suggests this:
Do all in your power; and all you ought to do, to have the matter
settled. From this we learn:
- That, in order to worship God acceptably, we must do justice to our fellow-men.
- Our worship will not be acceptable unless we do all we can to live peaceably with others.
- It is our duty to seek reconciliation with others when we have injured them.
- This should be done before we attempt to worship God.
- This is often the reason why God does not accept our offerings, and we go empty away from our devotions. We do not do what we ought to
others; we cherish improper feelings or refuse to make proper
acknowledgments, and God will not accept such attempts to worship him.