When I have old stained tea towels, hand towels, facecloths or dishcloths, I use them for rags. The way I identify them so I don't use them again for good linen is to cut the towels in half and cut the corners off the facecloths and dishcloths.
Old clothing can often be repurposed. One easy way is to cut the cloth into small rags. This is a page about make your own cleaning rags from old clothing.