The Greek that is translated as “shake off the dust from your feet” in English is translated in this occurrence in Matt. 10:14 as “shake off the dust from your feet to show renunciation” in Estado de México Otomi for clarification. In the other passages in Mark, Luke and Acts the Greek text gives a clarification as well. (Source: John Beekman in Notes on Translation, March 1965, p. 2ff.)
See also shake the dust off your feet.