What are you supposed to do about a mezuzah that was put up by a non-Jew? Do you need to take it down and put it back up? If so, do you recite a bracha? Does it matter if you own the house? rent the house? if the house belongs to a friend or relative?
The mezuzah should be taken down, and put up again with a berachah. If the house is yours, or you are renting it, you should do this on your own. If it belongs to a friend or relative, you can contact the owner and ask him if he wishes you to do it for him (as a shaliach). If he wishes, you can do it and make the berachah.
Sources: Although we find that a non-Jew is able to do tevilas keilim (Shulchan Aruch, Yoreh De’ah 120:15), and the Rashba (1:346) writes that he is also able to perform other mitzvos, it is possible that mezuzah, which is a mitzvah de’oraisah and requires propert intent (see Shulchan Aruch, Orach Chaim 60), cannot be achieved by a non-Jew. It is possible, however, that a non-Jew is able to perform the mitzvah of mezuzah for a Jew, just as we find that the milah of a non-Jew is valid (we assume with regard to the act of a mitzvah that the non-Jew had the correct intention).
Yet, it is certainly improper to fulfill the mitzvah by means of a non-Jew (see Shulchan Aruch 11:2, which cites Rambam who maintains that even if a Jew is present the non-Jew’s intention remains invalid — though there is room to distinguish tzitzis and mezuzah). To ensure that the mitzvah is performed properly, one should take it down and place it back on the doorpost. Because no berachah was originally made on the mezuzah, one should make a berachah upon re-affixing the mezuzah.