Probably best to contact the manufacturer for recommendation. However I just saw this on another discussion thread https://www.rugpadusa.com/

It depends on what kind of backing it has. If you haven’t heard of the knuckle test, try this. Pull the rug back to expose the reverse, with a bit of pressure, rub your knuckle across the underside. If it feels as if it’s going to tear your skin then it needs a pad. Otherwise it should be safe. I always but wool rugs that are hand tufted. Every one I’ve bought has the same type of reverse (consist across different manufacturers). I do not use padding with them currently. However, a more important question would be do you remove your shoes at the door? As with regular carpeting, sand and debris can make its way through the weave and if left unchecked I would be surprised if it didn’t cause scratches. I pull mine back and sweep underneath regularly. You’d be surprised how quickly stuff ends up there. Anyway, please see my pics attached.

Helpful. Thank

The wool rugs will most likely not ruin the floor, but "very small" rugs have a tendency to move/slip when walked on, so there is a chance of ruining someone's day with a fall.