I think you'll be pleasantly surprised- a good sponge and some barkeepers friend make quick work of scorched on oil, and usually leaves the pan looking new honestly.
Just be sure to get the powdered kind that comes in a cylindrical container, the liquid stuff in the plastic squeeze containers seems weaker and doesn't scrub stuff off as well in my experience. Did a great job of polishing tarnished copper pan bottoms though.
I had been meaning to get around to it forever but the bottom surface on this always stayed clean enough. Now that I got some I’m like everyone else who will tell you you should definitely get it.