I never use my shirt because I don't want it to get greasy. Use a small microfiber cloth and you can easily clean it. I use mine for my watch, glasses, tablet and smartphone. Sometimes I use antibacterial solution to clean my tablet/phone too.
I think that the touch screen sellers are really missing out on the business here, if some brand created a product to clean them it would be a great success. Those cloths are good tournique, I have to get one for myself.
Well, what could they sell? An ordinary piece of clothing to clean your touchscreen? Or just glasses cloth for the same use? Their target market would be full of fools.
I just use whatever cloth is available as well as long as I don't think it's rough or might damage my screen. I also just try and be gentle with it though sometimes I don't have anything to use other than just tissues which I am even more careful with. I think I'd be scared to use any fluid on my touch screen but I do use some water from time to time so I guess a specialized cleaning solution would be better.