From Rite of Penance, Chapter I, Rite for Reconciliation of Individual Penitents:
“PROCLAMATION OF PRAISE OF GOD AND DISMISSAL
47 . After the absolution, the priest continues:
Give thanks to the Lord, for he is good.
The penitent concludes: His mercy endures for ever.
Then the priest dismisses the penitent who has been reconciled, saying:
The Lord has freed you from your sins. Go in peace.”
This dismissal has no response. There are four other dismissal options in the book. One of them has the response “Amen” at the end. The others have no response. The one with the response is:
“ The Lord has freed you from sin.
May he bring you safely to his kingdom in heaven.
Glory to him for ever.
R. Amen.”
It has in n. 21:
“SHORTER RITE
21. When pastoral need dictates, the priest may omit or shorten some parts of the rite but must always retain in their entirety the penitent’s confession of sins and acceptance of the act of penance, the invitation to contrition (no. 45), and the formularies of absolution and dismissal.”
So “Give thanks to the Lord, for he is good” is optional. It is not a dismissal, but a Proclamation of Praise. The dismissal is required.
[Excerpts from the English translation of the Rite of Penance © 1974, International Commission on English in the Liturgy Corporation. All rights reserved.]