A removed strand will never be noticed. An optional approach is, with a razor, scrape off a little from the top of an out-of-the-way area. Discretely put a match to it. If the material burns to a powder, it is wool. If it melts, it is synthetic.
I haven't done this for many years, because there doesn't seem to be any need to know. Nearly all W@W carpeting is synthetic. A few area rugs are wool. If I were using a cleaning system that involved a lot of:
1. heat
2. water
3. high Ph (alkaline) cleaners
then I would want to know whether I was dealing with wool or a synthetic. But I'm not.
But there are purists out there who will differ violently with me on this position.