Jesus responds to the centurion's request.
He is a Savior who does not require worthiness in order to heal. The Jewish elders that the centurion sends to petition Jesus for a healing attest to the centurion's worthiness to have Jesus intercede (Lk. 7:5). The centurion himself proclaims his own unworthiness to have Jesus come under his roof (Lk. 7:6) and states that this conviction is why he did not petition Jesus directly but sent the elders. Judging by Jesus' distance healing, worthiness is not a prerequisite!
What impact is the story to have on listeners?
The idea of a centurion petitioning Jesus for a miracle would have been an "enormous surprise for the listener." She continues, "This begging by a centurion would humanize him for the listener. The situation shows a reversal, with the soldier, usually in a dominant position with the people, placing himself in a subservient position. (Cotter, 127)
Vestigius's glowing description of centurions that I mentioned earlier was not universally embraced. The popular perception of many centurions was that they were brawny, not too brainy, and often abusive of the citizenry. Bravery and group loyalty figured into their religious life. But their devotion to the Emperor and to various genii or spirits that protected the camp and them personally was motivated, not by a desire for salvation, but for protection in battle. And it would seem that Jesus is not criticizing that in this scene.
He's focused on the admirable factor in the centurion's petition: his faith that what Jesus commanded, Jesus enacted. Orders issued. Orders obeyed. If time allowed I would go into detail regarding Roman military religion and the role of faith in Jesus' miracles (since not all of them involve the faith of the petitioner). For this week, it will have to suffice to point out that, in this story, faith is faith.
And one more thing: This story has the kind of paradoxical punch the parables do—the Good Samaritan, the mustard seed as metaphor for kingdom of God, the devout and humble tax collector contrasted with the self-righteous Pharisee. Here we have a Roman soldier, of whom people would be rightly suspicious, displaying a confidence in Jesus as spiritual Commander that Jesus seems to find compelling.
The centurion may not embody all aspects of worthiness as listeners then would have defined it. But he does know a thing or two about confidence in the one giving him his orders. Do we?
Wendy Cotter, CSJ, The Christ of the Miracles Stories: Portrait through Encounter (Baker Academic Press, 2010).
For background on Roman military religion, see http://www.romanarmy.net/Religion.shtml
If you are interested in learning more about Roman military religion, see Robert Turcan's 1997 book, The Cults of the Roman Empire.