Thomas Aquinas

“ We must say, therefore, that grace was bestowed in circumcision as to all the effects of grace, but not as in Baptism. Because in Baptism grace is bestowed by the very power of Baptism itself, which power Baptism has as the instrument of Christ's Passion already consummated. Whereas circumcision bestowed grace, inasmuch as it was a sign of faith in Christ's future Passion: so that the man who was circumcised, professed to embrace that faith; whether, being an adult, he made profession for himself, or, being a child, someone else made profession for him. ”

“ But circumcision was an obligation imposed by the Law, according to Gal. 5:3: "I testify . . . to every man circumcising himself, that ne is a debtor to do the whole law." Therefore, if justice be by circumcision, "Christ died in vain," i.e. without cause. But this cannot be allowed. Therefore circumcision did not confer grace whereby the sinner is made righteous.
Objection 2: Further, before the institution of circumcision faith alone sufficed for justification; hence Gregory says (Moral. iv) : "Faith alone did of old in behalf of infants that for which the water of Baptism avails with us." ”

“ Just as before the institution of circumcision, faith in Christ to come justified both children and adults, so, too, after its institution. But before, there was no need of a sign expressive of this faith; because as yet believers had not begun to be united together apart from unbelievers for the worship of one God. It is probable, however, that parents who were believers offered up some prayers to God for their children, especially if these were in any danger. Or bestowed some blessing on them, as a "seal of faith"; just as the adults offered prayers and sacrifices for themselves. ”