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I am not an expert, but I learned enough to know that you will need to contact the cosmetic company directly for an answer. One of the ingredients - Tocopheryl acetate (Vitamin E) is often derived from wheatgerm. It is possible that they may have another source for it, but that needs to be confirmed.
Lush Cosmetics uses Tocopheryl acetate from a non-wheat source, but they are one of the few cosmetic companies that do (not all their products are gluten-free).
It is also possible that some of the other ingredients are derived from or contaminated with gluten - I have emailed companies for make-up options that I was certain would be safe as the ingredients were minimal and safe by themselves, but the replies indicated that the way the products were manufactured put them at risk for cross-contamination.