Luke uniquely said that these Jewish elders came to Jesus (οἱ δὲ παραγενόμενοι πρὸς τὸν Ἰησοῦν). They appealed or begged Jesus earnestly (παρεκάλουν αὐτὸν σπουδαίως). They said (λέγοντες) that this centurion was worthy of having Jesus grant this for him (λέγοντες ὅτι ἄξιός ἐστιν ᾧ παρέξῃ τοῦτο). Luke was the only one who had these elders recommend this Roman non-Jewish centurion for his consideration. Have you ever recommended someone as being worthy of a position?
This is something similar to Luke, chapter 8:31. Mark indicated that the demoniac begged, entreated, or beseeched Jesus many times (καὶ παρεκάλει αὐτὸν πολλὰ) not to send them (ἵνα μὴ αὐτὰ ἀποστείλῃ), the evil unclean spirits, away to another country, out of this country (ἔξω τῆς χώρας). Luke said that these evil spirits did not want to be sent into the abyss. They did not want to go anywhere. These evil spirits wanted to remain where they were, since they were content there.
After some of the Israelites died in the desert, others claimed to repent. They sought God earnestly as they remembered that God was their rock. The Most High God was their redeemer. They tried to flatter God with their mouths as they lied with their tongues. Their heart was not in it. They were not true to the covenant.