“treated…with contempt.” From exoutheneō (#1848 ἐξουθενέω). See commentary on 1 Thessalonians 5:20.
“mocked.” The Greek word translated “mocked” is empaizō (#1702 ἐμπαίζω), and means “mock,” “make fun of,” “ridicule.” See commentary on Matthew 27:29.
“sent him back to Pilate.” Herod Antipas was no doubt embarrassed by his failure to get Jesus to talk to him, so he mocked Jesus, treated him badly, and sent him to Pilate. He could have taken Jesus back to Galilee and tried him there, but since he was already feeling a lack of support from his subjects for killing John the Baptist, he would not take Jesus back to his area of strongest support and execute him when he could simply send him back to Pilate, who would then have to deal with him.