When is the supplication "My Lord, let me enter with a [truthful] entrance and exit with a [truthful] exit" recited, and is it recited upon a person's return to their homeland after travel?

There is no specific prophetic supplication (Du'a) authentically reported to be recited when settling in a place. However, the supplication "I seek refuge in the perfect words of Allah from the evil of what He created" (أعوذ بكلمات الله التامات من شر ما خلق) is general and can be recited in any place one sits or sleeps, and also when departing for travel. Furthermore, reciting "My Lord, enable me to alight at a blessed alighting, and You are the best of those who bring to alight" (رب أنزلني منزلا مباركًا وأنت خير المنزلين) and "My Lord, cause me to enter a truthful entrance" (رب أدخلني مدخل صدق) is recommended when overseeing a home, and is also suitable because it expresses truthfulness and righteousness in travels and reliance upon Allah. 'Umar ibn 'Abd al-'Aziz used to recite a lengthy supplication upon entering his home, in which he sought provision and protection.