Is the black Apple cloth that comes with the MacBook Pro ok for cleaning iPhone and Mac screens? I use it regularly to clean my rmbp screen, and I've noticed a small scratch on the black panel few days ago, I thought it might be because I've used tap water or it was there and I didn't notice it.

Now I used it to clean a second hand iPhone. I bought before putting a protective guard on, and after I cleaned it I noticed small scratches and I don't know if they were there or not (the seller had it for about 3 years, so it could have had scratches and I didn't see them because the screen wasn't clean).

Is the cloth microfiber and is it ok to use it to clean screens?
It should be fine.. I would suggest washing it as there may be small dust particles on it, which could potentially be causing those screen scratches.