It's ridiculous how much people spend on detergents and other cleaning products.
Cast iron can be polished clean with one of the best kitchen scrubs: salt.
First clean the pan the usual way. Dry it and then pour a bit of salt on the bottom and use a cloth or brush to clean the pan with the salt.
When the dirt has come off, clean the pan and rinse with a lot of water.
Then fatten the pan with a bit of oil before putting it away.