Honestly, I wouldn't touch the inside central part of that lid. The end caps ? Sure, take a wire wheel or brush to them. You could disassemble the lid to make it easier. The inside center of that lid isn't SS. It's a steel liner that can, and does rust/corrode. Long story short, it's nicely seasoned the way it is. If you think something "dirty" is there, wipe with some Simple Green or something similar and then rinse. The loose/flaky stuff is carbon as Heyjude and Nitis said. Just scrape off what you can.