Luke uniquely said that these Jewish elders continued praising this centurion, who loved the Jewish people, their people (ἀγαπᾷ γὰρ τὸ ἔθνος ἡμῶν). He had built a synagogue for them (καὶ τὴν συναγωγὴν αὐτὸς ᾠκοδόμησεν ἡμῖν). There were many instances of Roman soldiers adopting the religious practices of the people where they were staying. However, building a synagogue seems a bit much. It may have led to better community relations. Although he was not Jewish, this centurion had been very favorable to the Jewish people by helping them build a new synagogue. There was no mention of this synagogue in the Matthew story about the centurion. Would you be favorable to a religion not your own?
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?