I think the OP is referring to polishing the lyre profile of the case (the surface between the side and the top facet). OP is correct this part should be polished (notice the first photo the area between the pushers that still retains polished).
To OP: I'd only try the least amount of polishing e.g. cape cod polishing cloth and try to match the shinier look of the finish of that small area between the pushers.
PS: I believe the seller is an active OF member.
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