(Note: This is a major question - as are all matters of food and mitzvah articles – and it should not be taken lightly. In particular, tzitzis have two major requirements with respect to their kashrus, neither of which can be seen or measured: 1) the strings themselves must be spun and twisted ‘lishmah’ (i.e. with the express intent of the craftsman to create kosher mitzvah articles) and 2) the tzitzis must be tied onto the garment ‘lishmah’ as well. Thus, even if visibly the tzitzis look kosher, they may, in fact, not be at all!)
Answer: The basic premise is that we must rely on the integrity of an honest, skilled and G-d-fearing Jew. We cannot trust the workmanship of a non-Jew or even a Jew who is suspect of halachic impropriety. That said, halacha does recognize the universal business-sense of people. It knows that a businessman would not wittingly 0undermine his own interests. So, suppose a non-Jewish distributor advertises that he buys religious merchandise from a certain reliable Jewish manufacturer. Halacha allows us to believe the non-Jew, on the assumption that he would not lie, knowing that disclosure would cost him his reputation and livelihood. If the seller does not have his reputation at stake (i.e. he is not a merchant or he claims to have made the tzitzis himself), then he has no credibility and cannot be relied upon.
(Note: The same way we must take precautions with sellers, so must we take precaution with those who handle and transport the mitzvah articles. Shulchan Aruch, in the section dealing with halachos of Kashrus, provides specific guidelines for the proper sealing and marking (Heb: ‘simanim’ - sings) of kosher food and mitzvah articles during transit and handling.
Watch who you give it to!
In earlier times and places, Jews were not permitted to entrust tzitzis to the hands of non-Jews. It was not uncommon for a non-Jew to disguise himself as a Jew by donning tzitzis, for the purpose of infiltrating Jewish communities in order to steal and murder! Alternatively, non-Jews would offer Jewish religious articles as barter for immoral purposes (e.g. harlotry). Imagine the Chilul Hashem (desecration of Hashem’s Name) generated when people would presume that the promiscuous customers were Jews! Thankfully these concerns (esp. the first) do not exist in our times in civilized lands such as ours, and halacha has relaxed this restriction.