The Greek that is typically translated in English as “shake the dust off your feet as a testimony against them” (Luke 9:5) is translated by the Italian La Sua Parola è Vita translation more explicitly as lasciandola scuotete la polvere dai vostri piedi per mostrare che non avete più niente a che fare con loro e li lasciate al loro destino or “shake the dust off your feet to show that you do not have anything more to do with them and that you leave them to their fate.”
Luke 10:11, translated in English as “Even the dust of your town that clings to our feet, we wipe off in protest against you” or similar is strangulated as Non abbiamo più niente a che fare con voi e vi lasciamo al vostro destino. Ecco, riprendetevi anche la polvere della vostra città or “We do not have anything more to do with you and leave you to your fate. Here, take back also the dust of your city.”
Source: Cotrozzi 2019
See also shake off the dust from your feet.