Exegesis:

hosoi an mē dechōntai humas lit. ‘as many as do not welcome you,’ i.e. ‘as for all those who do not welcome you’ (cf. Translator’s New Testament, New English Bible). The relative pronoun hosoi is not taken up by a corresponding demonstrative pronoun, but indirectly by tēs poleōs ekeinēs ‘that town.’ This shows that the clause hosoi … humas does not refer to the negative reactions of individuals but to the population of a certain town, or, towns, as a whole.

exerchomenoi apo tēs poleōs ekeinēs lit. ‘when you leave that town’ (cf. New English Bible); with a shift to an imperative because of apotinassete “leave that town” (Phillips).

ton koniorton apo tōn podōn humōn apotinassete ‘shake the dust off your feet,’ cf. 10.11.

koniortos (also 10.11) ‘dust,’ refers here to the dust in the streets.

apotinassō ‘to shake off.’

eis marturion ep’ autous ‘as a testimony against them.’ The shaking off of the dust serves as a demonstration, or, a warning, or, a protest against those who do not receive the disciples.

Translation:

Wherever they do not receive you, or, ‘in a town where they do not receive you,’ ‘if the people/inhabitants of a town reject you.’ The verb to receive is used with personal object in the sense of ‘to let a person come to one’; hence, ‘to allow a person to approach’ (in 15.2), ‘to welcome a person (to one’s house, or, as one’s guest)’ (9.5; 10.38; 16.4, 9, and cf. on “welcomed” in 8.40), which may imply readiness to help (a child, 9.48a), or, when Jesus or his disciples are the guests, acceptance of and obedience to their words (9.48b; 10.8, 10; 19.6).

When you leave that town shake …, preferably two imperatives, ‘leave (or, go away from) that town and shake…,’ or, better to bring out the simultaneousness, “leave their town, and as you do so shake…” (The Four Gospels – a New Translation). For town cf. on “city” in 1.26.

Shake off the dust from your feet. The expression, as used by Jesus, is not a metaphor but refers to a well known custom, which may best be rendered literally. For a footnote, if required, cf. Plummer’s “It signified that henceforth they had not the smallest thing in common with the place”. — Shake, or, ‘dust off’ (Shona 1966), ‘wipe off,’ if that is the more common gesture (Balinese, similarly Marathi). Dust. In some languages the same or cognate words are used to refer to ‘dust’ and to ‘ash’ (Tae,’ Sundanese), or to ‘dust’ and to ‘powder/pollen’ (Batak Toba, cf. Malay); in Toraja-Sa’dan the word lit. means ‘what-is-like-husked-rice.’ The phrase from your feet is in some cases better taken with the noun, e.g. ‘the dust on your feet, or, that sticks to your feet’ (cf. e.g. Trukese, Malay). Instead of ‘your feet’ one may have to use ‘the soles of your feet’ (e.g. in Toraja-Sa’dan), cf. also ‘from underneath of your feet’ (Kituba).

As a testimony against them, serving to indicate the meaning of the gesture just mentioned. Some more meaningful renderings are, ‘as-breaking-off sign against those people’ (Balinese, making use of a term commonly referring to the severing of relationships), ‘to denounce (lit. to say-to-be-mistaken-to) those people’ (Tae’ 1933), ‘that it will be a sign of accusation to-them’ (Trukese).

Quoted with permission from Reiling, J. and Swellengrebel, J.L. A Handbook on the Gospel of Luke. (UBS Handbook Series). New York: UBS, 1971. For this and other handbooks for translators see here . Make sure to also consult the Handbook on the Gospel of Mark for parallel or similar verses.