Is this Tribunal of Penance REQUIRED for forgiveness of sins by the church?
For the forgiveness of mortal sins, yes. Those who despise Christ's appointed means of salvation cannot be saved.
St. Thomas, III q. 84 a. 5Whether this sacrament is necessary for salvation?
Objection 1. It would seem that this sacrament is not necessary for salvation. Because on Ps. 125:5, "They that sow in tears," etc., the gloss says: "Be not sorrowful, if thou hast a good will, of which peace is the meed." But sorrow is essential to Penance, according to 2 Cor. 7:10: "The sorrow that is according to God worketh penance steadfast unto salvation." Therefore a good will without Penance suffices for salvation.
Objection 2. Further, it is written (Proverbs 10:12): "Charity covereth all sins," and further on (Proverbs 15:27): "By mercy and faith sins are purged away." But this sacrament is for nothing else but the purging of sins. Therefore if one has charity, faith, and mercy, one can obtain salvation, without the sacrament of Penance.
Objection 3. Further, the sacraments of the Church take their origin from the institution of Christ. But according to John 8 Christ absolved the adulterous woman without Penance. Therefore it seems that Penance is not necessary for salvation.
On the contrary, our Lord said (Luke 13:3): "Unless you shall do penance, you shall all likewise perish."
I answer that, A thing is necessary for salvation in two ways: first, absolutely; secondly, on a supposition. A thing is absolutely necessary for salvation, if no one can obtain salvation without it, as, for example, the grace of Christ, and the sacrament of Baptism, whereby a man is born again in Christ. The sacrament of Penance is necessary on a supposition, for it is necessary, not for all, but for those who are in sin. For it is written (2 Paral 37 [The prayer of Manasses, among the Apocrypha), "Thou, Lord, God of the righteous, hast not appointed repentance to the righteous, to Abraham, Isaac and Jacob, nor to those who sinned not against Thee." But "sin, when it is completed, begetteth death" (James 1:15). Consequently it is necessary for the sinner's salvation that sin be taken away from him; which cannot be done without the sacrament of Penance, wherein the power of Christ's Passion operates through the priest's absolution and the acts of the penitent, who co-operates with grace unto the destruction of his sin. For as Augustine says (Tract. lxxii in Joan. [Implicitly in the passage referred to, but explicitly Serm. xv de verb Apost.), "He Who created thee without thee, will not justify thee without thee." Therefore it is evident that after sin the sacrament of Penance is necessary for salvation, even as bodily medicine after man has contracted a dangerous disease.
Reply to Objection 1. This gloss should apparently be understood as referring to the man who has a good will unimpaired by sin, for such a man has no cause for sorrow: but as soon as the good will is forfeited through sin, it cannot be restored without that sorrow whereby a man sorrows for his past sin, and which belongs to Penance.
Reply to Objection 2. As soon as a man falls into sin, charity, faith, and mercy do not deliver him from sin, without Penance. Because charity demands that a man should grieve for the offense committed against his friend, and that he should be anxious to make satisfaction to his friend; faith requires that he should seek to be justified from his sins through the power of Christ's Passion which operates in the sacraments of the Church; and well-ordered pity necessitates that man should succor himself by repenting of the pitiful condition into which sin has brought him, according to Prov. 14:34: "Sin maketh nations miserable"; wherefore it is written (Sirach 30:24): "Have pity on thy own soul, pleasing God."
Reply to Objection 3. It was due to His power of "excellence," which He alone had, as stated above (64, 3), that Christ bestowed on the adulterous woman the effect of the sacrament of Penance, viz. the forgiveness of sins, without the sacrament of Penance, although not without internal repentance, which He operated in her by grace.