ou should be using a stiff, plastic bristle brush. Until the patina is really baked in after months of use, it can be removed with metalic cleaning implements such as wire brush, steel wool, stainless steel scouring pads, sand, and some cleaners such as Comet.
Remember that the patina is backed on grease, that polymerizes into a hard, slippery, carbon surface. Carbon is softer than is steel. The good thing is that you can re-season the pan.
After re-seasoning the pan, use hot water and a plastic brush to clean. Dry with paper towels, or over a medium flame, then rub a sheen of oil or grease onto the cooking surface before putting the pan away.
After several meals, you will find that like my own CI, it is virtually stick free, like the best non-stick you can purchase. It's a bit of work, but once done, the pan will last a couple lifetimes, and will work with any heat source and food type. What else can you ask from a frying pan?
Seeeeeya; Goodweed of the North