In the tridentine rite, the priest held up the consecrated host, saying (in Latin) “Behold the Lamb of God, behold him who takes away the sins of the world.” The people responded, “Lord, I am not worthy that you should come under my roof. But only say the word and my soul shall be healed.”
The response echoed the words of the Roman centurion who asked for his son’s healing, but said he was not worthy that Christ should come into his house; but that Jesus need only speak the word of command from a distance. Jesus commended him for his remarkable faith.
So the Mass response was intended to show both our faith, and our need of healing, by evoking the words of the centurion from scripture.
When the Mass rite was revised, the response was simplified to: “Lord, I am not worthy to receive you, but only say the word and I shall be healed.” Which is not much of a change, but probably fails to recall to us the scripture passage of the centurion.
JimG