Actually, it doesn't. If the cast iron is cold, the pores in the iron are not open and a SMALL amount of something like Dawn on a sponge will cut the grease and won't affect the seasoning. Reheat to dry and give a quick rub with some veg oil on a paper towel. I clean mine that way and they are super non-stick.
I've heard of the oil and salt routine. I'll have to try that next time to compare.
My 1st husband unseasoned that skillet the first month we were married-I had to season it all over again, and I’ve never let anyone else use it again-not even the cub. When I was 15, my grandmother gave the skillet and some other utensils that were in common use by Tejana women on ranches when she was young-it was a present for my birthday.