There are specific ways for you to clean aluminum and stainless steel (which are the most common types of cookware that you will find in these kits) but using steel wool may not be one of them. Steel wool is a very abrasive substance that is a little too intense for these types of materials. If you do so with either stainless steel or aluminum, the wool will scratch the surface.
Not only will this not look good, but you also risk compromising the effectiveness of the cookware. Also, specifically with stainless steel, if you scratch the surface with steel wool than it becomes more susceptible to stains and rust. Just stick with a sponge and your two haymakers to clean the cookware!