How do I get this green and crusted inside part off?

 

You don't. Just get a new/rebuilt distributor.

 

Need to pull the distributor, push out the roll pin retaining the gear and pull the shaft. There is a one-time-use clip that retains the shield. Under the shield is the pickup coil. A new one includes a new clip to retain it and the shield.

If that is a GM ICM I would get a new shaft (includes the star wheel) and a new pickup and continue to use that distributor. If it isn't a GM ICM add that to the list of items to replace.

Varnish build up on the shaft can make it difficult to remove. A carb gum cutter such as 2+2 makes short work of it.

RBob.