What ingredients make powdered sugar not gluten-free?
The simple answer to your question is the kind of starch they use. Most use cornstarch or tapioca starch, neither of which contain gluten, so most powdered sugar shouldn't contain gluten. If the type of starch isn't listed, don't buy that product.

For absolutely no gluten, it gets a bit more complicated.

A Google search for "Gluten Free Powdered Sugar" only yielded a few brands that make a "gluten-free" claim. Since most brands of powdered sugar don't contain any ingredients that would normally contain gluten, look for the line "This product is processed in a facility that also processes wheat". Choose a powdered sugar that lists the starch used as cornstarch, tapioca starch or other non-gluten starch and that doesn't have that line on the label. Of course I can only speak to US labeling, other countries may be different.

One brand, Domino Sugar, stood out to really stand by their claim of gluten free.  Domino's Gluten Free Claim  (C&amp;H is Domino, BTW). I happen to have some C&amp;H powdered sugar, so I looked at the label. There is no "Gluten-Free" claim on the label, but the ingredients listed are only sugar and corntarch, and there is no "this product is processed in a facility..." warning. Walmart brand also pops up on the "Gluten Free Powdered Sugar" search, they say "Naturally gluten-free food". The FDA requires that claim not be misleading, so if they do use equipment to process the sugar that also processes gluten-containing ingredients, the sugar cannot contain more that 20 ppm gluten.

There is one way to know for sure about any ingredient you use, or to even to check your final dish. Elisa Technologies, a very well respected name in medical laboratory testing, has put out home test strips sensitive to 10 ppm, that's half the concentration of gluten the FDA allows for a product to be certified "gluten-free".  If a product tested contains less than 20 ppm gluten the US, Canada and the European Union allow that product to use "Gluten Free" on the label. FDA Announcement At over $10 a strip, you'd want to use them judiciously, but if I or someone I loved had serious health issues that did not allow gluten, I'd get these strips. Test Strips