Nothing that looks unusual, and is marked in any way with Sturm, should be thought of as original. While Gulf is correct that they did put their marks on genuine stuff for a time (they still are a major surplus wholeseller last I checked), something like this should be treated as suspect until otherwise verified. Especially brand new looking items.
In this case, it's definitely a fantasy item. I've never seen one of these before, but there are tons of fake FJ helmet covers out there in various cloth. Since this is obviously made from the same cloth that Sturm used for thousands of hats (they were making them back in the 1980s, BTW), and I don't know of any legitimate items made from it, that right there makes it suspect. Aside from that, I've never seen BGS use helmet covers at all from 1950s-1970s except for taking the Splintertarn hoods from the very early Zeltbahns and using those during field exercises. That's some 20 years prior to GSG-9. Since then, however, GSG-9 did use various camouflage and then solid color helmet covers on their titanium helmets. The new German Federal Police (what used to be BGS) only use solid color helmet covers as far as I know.
There's also berets out there in Flecktarn, Sumpftarn, and Amoebatarn. All professionally made and the Amoebatarn ones come complete with genuine 1950s/1960s M43 hat badges. There's also M43 hats just like that as well.
Hats, helmet covers, and berets are all relatively cheap items to make and have good markets. They also economize the use of cloth, which means you get a lot more out of spare cloth (especially old Zeltbahns) than you do for other items. Less waste = more profits! It's why there is so much activity with these items and not so much with uniforms.
Lots of stuff out there to beware of, but a drop in the bucket compared to the 3rd Reich stuff