It is. The doctrine is perfectly reasonable. To understand the issue it's important to understand what an indulgence is.
Consider the following sin. A boy bats a baseball through his neighbor's window. He runs away. Later, he regrets running away, goes to his neighbor, and apologizes. The neighbor accepts his apology. This scenario is analogous to the Catholic practice of Confession. The neighbor represents God who acts through the priest in forgiving the sinner (the boy).
But is simple forgiveness of the boy by the neighbor sufficient for the reparation of the wrong? Shouldn't the boy repay the neighbor for the broken window, in addition to asking for forgiveness? So "an indulgence is a remission of the temporal punishment due to sin, the guilt of which has been forgiven."
Indlugences, from the Catholic Encyclopedia:
The word indulgence (Lat. indulgentia, from indulgeo, to be kind or tender) originally meant kindness or favor; in post-classic Latin it came to mean the remission of a tax or debt. In Roman law and in the Vulgate of the Old Testament (Isaiah 61:1) it was used to express release from captivity or punishment. In theological language also the word is sometimes employed in its primary sense to signify the kindness and mercy of God. But in the special sense in which it is here considered, an indulgence is a remission of the temporal punishment due to sin, the guilt of which has been forgiven. Among the equivalent terms used in antiquity were pax, remissio, donatio, condonatio.See also Indulgences, Catechism of the Catholic Church (beginning at paragraph 1471).WHAT AN INDULGENCE IS NOT
To facilitate explanation, it may be well to state what an indulgence is not. It is not a permission to commit sin, nor a pardon of future sin; neither could be granted by any power. It is not the forgiveness of the guilt of sin; it supposes that the sin has already been forgiven. It is not an exemption from any law or duty, and much less from the obligation consequent on certain kinds of sin, e.g., restitution; on the contrary, it means a more complete payment of the debt which the sinner owes to God. It does not confer immunity from temptation or remove the possibility of subsequent lapses into sin. Least of all is an indulgence the purchase of a pardon which secures the buyer's salvation or releases the soul of another from Purgatory. The absurdity of such notions must be obvious to any one who forms a correct idea of what the Catholic Church really teaches on this subject.
WHAT AN INDULGENCE IS
An indulgence is the extra-sacramental remission of the temporal punishment due, in God's justice, to sin that has been forgiven, which remission is granted by the Church in the exercise of the power of the keys, through the application of the superabundant merits of Christ and of the saints, and for some just and reasonable motive.
Regarding this definition, the following points are to be noted:
In the Sacrament of Baptism not only is the guilt of sin remitted, but also all the penalties attached to sin. In the Sacrament of Penance the guilt of sin is removed, and with it the eternal punishment due to mortal sin; but there still remains the temporal punishment required by Divine justice, and this requirement must be fulfilled either in the present life or in the world to come, i.e., in Purgatory. An indulgence offers the penitent sinner the means of discharging this debt during his life on earth. Some writs of indulgence--none of them, however, issued by any pope or council (Pesch, Tr. Dogm., VII, 196, no. 464)--contain the expression, "indulgentia a culpa et a poena", i.e. release from guilt and from punishment; and this has occasioned considerable misunderstanding (cf. Lea, "History" etc. III, 54 sqq.). The real meaning of the formula is that, indulgences presupposing the Sacrament of Penance, the penitent, after receiving sacramental absolution from the guilt of sin, is afterwards freed from the temporal penalty by the indulgence (Bellarmine, "De Indulg"., I, 7). In other words, sin is fully pardoned, i.e. its effects entirely obliterated, only when complete reparation, and consequently release from penalty as well as from guilt, has been made. Hence Clement V (1305-1314) condemned the practice of those purveyors of indulgences who pretended to absolve" a culpa et a poena" (Clement, I. v, tit. 9, c. ii); the Council of Constance (1418) revoked (Sess. XLII, n. 14) all indulgences containing the said formula; Benedict XIV (1740-1758) treats them as spurious indulgences granted in this form, which he ascribes to the illicit practices of the "quaestores" or purveyors (De Syn. dioeces., VIII, viii. 7).
The satisfaction, usually called the "penance", imposed by the confessor when he gives absolution is an integral part of the Sacrament of Penance; an indulgence is extra-sacramental; it presupposes the effects obtained by confession, contrition, and sacramental satisfaction. It differs also from the penitential works undertaken of his own accord by the repentant sinner -- prayer, fasting, alms-giving -- in that these are personal and get their value from the merit of him who performs them, whereas an indulgence places at the penitent's disposal the merits of Christ and of the saints, which form the "Treasury" of the Church.
An indulgence is valid both in the tribunal of the Church and in the tribunal of God. This means that it not only releases the penitent from his indebtedness to the Church or from the obligation of performing canonical penance, but also from the temporal punishment which he has incurred in the sight of God and which, without the indulgence, he would have to undergo in order to satisfy Divine justice. This, however, does not imply that the Church pretends to set aside the claim of God's justice or that she allows the sinner to repudiate his debt. As St. Thomas says (Suppl., xxv. a. 1 ad 2um), "He who gains indulgences is not thereby released outright from what he owes as penalty, but is provided with the means of paying it." The Church therefore neither leaves the penitent helplessly in debt nor acquits him of all further accounting; she enables him to meet his obligations.
In granting an indulgence, the grantor (pope or bishop) does not offer his personal merits in lieu of what God demands from the sinner. He acts in his official capacity as having jurisdiction in the Church, from whose spiritual treasury he draws the means wherewith payment is to be made. The Church herself is not the absolute owner, but simply the administratrix, of the superabundant merits which that treasury contains. In applying them, she keeps in view both the design of God's mercy and the demands of God's justice. She therefore determines the amount of each concession, as well as the conditions which the penitent must fulfill if he would gain the indulgence.
Sure the boy (or sinner) should do restitution or pay back for wrongs done when/if possible.
However, paying back God? Don't think so.