Cleaning iPad Pro Screen

After using my iPad Pro for about a year, I started to have trouble with the Apple pencil making stray marks, usually huge lines, but often several small marks as well. I eventually figured out that I needed to clean my screen. Indeed, when I really looked carefully I could see that the screen had picked up bits of dust and cat hairs from the inside of the case, which folds back and acts as a stand. When in this position the inside of the case is sitting on my desk. I was wondering if anyone else had this problem, and if just wiping with a cloth is helpful. I'm concerned that the debris will stick to the cloth and accumulate, just to make things worse down the line. Are there good disposable wipes? Can the microfiber cloths be washed?