Do you mean towel or cloth? Cloth would seem to be a better word. A towel suggests a thick, fluffy object used to dry our face and bodies. We use cloths, not towels, for cleaning things. A towel would be too thick and may leave fluff behind. The first sentence is confusing - are these two different processes? Are we supposed to use just water? Or detergent? Are they alternatives? It might be better to split them into two sentences: "Wipe the outside of the product with a soft damp cloth. If needed, use a mild detergent and then dry with a clean cloth to avoid leaving any stains." Note that you can't wipe with a brush. It would be better to say 'use' here. Also note that the substances (toothpaste, thinners etc) in brackets are not examples of detergents. A detergent is a specific type of surfactant, used for washing dishes, laundry etc. You need a more general term here. 'This' would be preferable to 'It' in the last sentence.

I think I understand it. It seems fine. When you say "clean towel" do you mean "not soaked in water" (dry)? "and wipe it with a clean towel" - is the intention 'then wipe it with a clean towel" ... ie after the wet towel?