Serious buildup outside of cast iron skillet
The inside looks absolutely fine, so assuming you will protect that if you do any actual work on the outside I see a couple of routes you can take...


You can ignore it &amp; see if it will reach a new equilibrium with your own cooking equipment &amp; technique.
You can clean it off &amp; quite quickly return the outside to a lesser seasoned state - as you're not cooking on the outside the seasoning is far less important, &amp; as you've already discovered, the outsides of pans can get a lot more build-up over time than the insides*.
You could attack it with sandpaper, or a drill &amp; wire brush attachment, though you need to beware of the mess that can make if you do it indoors... or you could take it to somewhere that could shot-blast it for you. This is an industrial cleaning process, depending on abrasive type can be extremely vicious, but it's rapid &amp; they could clean the outside back to shiny iron in 2 minutes.


You can then re-season the outside.

*You should have seen my old wok before my partner threw it away. I eventually forgave her ;)