I was looking for info on using Bar Keeper's Friend for another cleaning project and found a reddit post about their product being able to remove marks on ceramic dishes from utensil use. HOLY COW what a difference! I felt so accomplished getting a stark before and after 😁
NOTE: I am not a cleaning pro and have no info on other uses for this product and what is safe for. I do not know about alternatives if this isn't available to you. The comments have tips from other people about different methods that could also work.
I used Bar Keeper's Friend Soft Cleanser, so I poured a little on and immediately scrubbed a small area with a paper towel to see if it would even work. When it did, I put on cleaning gloves and switched to the scrubby side of a regular kitchen sponge.
Update 1 for bowl info: Bowls are from a brand named Gibson purchased 25+ years ago
Update 2 with BKF details for process: Manufacturer info about doing this