At Serious Eats, Kenji López-Alt sets the record straight about some misconceptions people have about cast iron pans.
The Theory: Seasoning is a thin layer of oil that coats the inside of your skillet. Soap is designed to remove oil, therefore soap will damage your seasoning.
The Reality: Seasoning is actually not a thin layer of oil, it’s a thin layer of polymerized oil, a key distinction. In a properly seasoned cast iron pan, one that has been rubbed with oil and heated repeatedly, the oil has already broken down into a plastic-like substance that has bonded to the surface of the metal. This is what gives well-seasoned cast iron its non-stick properties, and as the material is no longer actually an oil, the surfactants in dish soap should not affect it. Go ahead and soap it up and scrub it out.
I have two cast iron pans, including this skillet I use almost exclusively for making the world’s best pancakes. Although, after hearing from Kenji that vintage cast iron pans can be slight better than modern pans, I might seek a replacement on Etsy. See also how to season a cast iron pan.