1 sn To shake the dust off represented shaking off the uncleanness from one’s feet; see Luke 10:11; Acts 13:51; 18:6. It was a sign of rejection.
2 sn Most read your sons as a reference to Jewish exorcists (cf. “your followers,” L&N 9.4), but more likely this is a reference to the disciples of Jesus themselves, who are also Jewish and have been healing as well (R. J. Shirock, “Whose Exorcists are they? The Referents of οἱ υἱοὶ ὑμῶν at Matthew 12:27/Luke 11:19,” JSNT 46 [1992]: 41-51). If this is a reference to the disciples, then Jesus’ point is that it is not only him, but those associated with him whose power the hearers must assess. The following reference to judging also favors this reading.
3 tn The pronoun “them” is not in the Greek text, but is implied. Direct objects were frequently omitted in Greek when clear from the context.