First, there's far more to the design and construction of a jacket than just the materials. So even if the jacket used genuine Gore-Tex material, I'd be suspicious of overall quality in such an inexpensive product.
Second, not only does fake Gore-Tex exist, but so do fake name branded clothes. So even if you buy a well-known name branded that used genuine Gore-Tex material, the garment itself could be fake.
Probably the most reliable way to avoid fakes is to buy from reputable retailers.
Another suggestion is to use Google Search on the specific make of clothing along with the keyword "fake." There are many results, articles, videos, etc. that will help you distinguish fakes from the genuine article.
Finally, W L Gore Corp, the maker of Gore-Tex offers to help identify if specific items are genuine.
one or more gifts or other benefits from the co-op.