The best way to clean a cast-iron drop in bathtub is with warm soapy water and a soft cloth. Avoid scraping tools and steel wool, as they may irreparably damage the surface of the bathtub.
Conventional bathtub cleaning products may also be too harsh due to their acid content, so read their instructions carefully or avoid them entirely. Cleaning a cast iron bathtub with gentle cleaning supplies may take longer than a typical fiberglass or ceramic bathtub, but the effort is worth it.
If you are going to use a new cleaning product on the tub for the first time, try it out on a small patch in a discrete area to monitor for damage to the tub’s finish.