982. There is no offence, however serious, that the Church cannot forgive. "There is no one, however wicked and guilty, who may not confidently hope for forgiveness, provided his repentance is honest.⁵²⁷ Christ who died for all men desires that in his Church the gates of forgiveness should always be open to anyone who turns away from sin.⁵²⁸

 

2227. Children in turn contribute to the growth in holiness of their parents.³⁶ Each and everyone should be generous and tireless in forgiving one another for offences, quarrels, injustices, and neglect. Mutual affection suggests this. the charity of Christ demands it.³⁷

 

2845. There is no limit or measure to this essentially divine forgiveness,¹⁴⁶ whether one speaks of "sins" as in Luke (11:4), "debts" as in Matthew (6:12). We are always debtors: "Owe no one anything, except to love one another."¹⁴⁷ The communion of the Holy Trinity is the source and criterion of truth in every relationship. It is lived out in prayer, above all in the Eucharist.¹⁴⁸

982. There is no offence, however serious, that the Church cannot forgive. "There is no one, however wicked and guilty, who may not confidently hope for forgiveness, provided his repentance is honest.⁵²⁷ Christ who died for all men desires that in his Church the gates of forgiveness should always be open to anyone who turns away from sin.⁵²⁸

2227. Children in turn contribute to the growth in holiness of their parents.³⁶ Each and everyone should be generous and tireless in forgiving one another for offences, quarrels, injustices, and neglect. Mutual affection suggests this. the charity of Christ demands it.³⁷

2845. There is no limit or measure to this essentially divine forgiveness,¹⁴⁶ whether one speaks of "sins" as in Luke (11:4), "debts" as in Matthew (6:12). We are always debtors: "Owe no one anything, except to love one another."¹⁴⁷ The communion of the Holy Trinity is the source and criterion of truth in every relationship. It is lived out in prayer, above all in the Eucharist.¹⁴⁸

Matthew 18:21-22 is referenced at three places in the Catechism of the Catholic Church, and I've emphasised the parts relevant to this view. In each, it is emphasised that forgiveness should be limitless.

³⁶ Gaudium et Spes 48 #4
³⁷ Cf. Mt 18:21-22; Lk 17:4
¹⁴⁶ Cf. Mt 18:21-22; Lk 17:3-4
¹⁴⁷ Rom 13:8
¹⁴⁸ Cf. Mt 5:23-24; 1 Jn 3:19-24
⁵²⁷ Roman Catechism I, 11, 5 (Catechism of Trent)
⁵²⁸ Cf. Mt 18:21-22

Matthew 18:21-22 is referenced at three places in the Catechism of the Catholic Church, and in each place it supports this view (I've emphasised the relevant parts). The Church teaches that forgiveness should be limitless, and "seventy times seven" effectively means "infinity".

This is a theme Pope Francis took up with the Bull of Indiction for the Jubilee Year of Mercy, in which he exhorts the faithful to be merciful and forgiving. "Blessed are the merciful, for they shall obtain mercy" which has a parallel in the Lord's Prayer itself, "Forgive us our trespasses as we forgive those who trespass against us." If we are to trust in the limitless forgiveness of God, we must emulate that ourselves.

In the parables devoted to mercy, Jesus reveals the nature of God as that of a Father who never gives up until he has forgiven the wrong and overcome rejection with compassion and mercy. ... Jesus affirms that mercy is not only an action of the Father, it becomes a criterion for ascertaining who his true children are. In short, we are called to show mercy because mercy has first been shown to us. Pardoning offences becomes the clearest expression of merciful love, and for us Christians it is an imperative from which we cannot excuse ourselves. At times how hard it seems to forgive! And yet pardon is the instrument placed into our fragile hands to attain serenity of heart. To let go of anger, wrath, violence, and revenge are necessary conditions to living joyfully. Let us therefore heed the Apostle’s exhortation: “Do not let the sun go down on your anger” (Eph 4:26). Above all, let us listen to the words of Jesus who made mercy an ideal of life and a criterion for the credibility of our faith: “Blessed are the merciful, for they shall obtain mercy” (Mt 5:7): the beatitude to which we should particularly aspire in this Holy Year.^A

³⁶ Gaudium et Spes 48 #4
³⁷ Cf. Mt 18:21-22; Lk 17:4
¹⁴⁶ Cf. Mt 18:21-22; Lk 17:3-4
¹⁴⁷ Rom 13:8
¹⁴⁸ Cf. Mt 5:23-24; 1 Jn 3:19-24
⁵²⁷ Roman Catechism I, 11, 5 (Catechism of Trent)
⁵²⁸ Cf. Mt 18:21-22
^A Misericordiae Vultus 9