They would probably be able to get a sample of the granite from a tombstone company to ‘practice’ on, providing they can determine what kind of oil (cooking? it looks clear to me from the pics) was used, and what might remove it from the engraved portion of the granite, if that is even possible.
Unfortunately, I think the whole wall panels would have to be replaced. :*(
“Clear” as in ‘not dark like motor oil or something’, not ‘clear’ as in ‘I totally know what I’m talking about’.
In addition, the poster mentioned that the polished portions looked "cloudy"...meaning that the polished finished may have been removed or damaged; one can easily do that with many substances. This creates a major problem, because although it can be "repolished" those areas would then not necessarily match the rest of the panels which have had the "wear and tear" of wind, rain, and time.
They probably haven't done anything, because it will take an expert in this field to survey the damage and suggest a solution. While you can call a guy out of the phone book to repair your kitchen counter, this is a huge National Monument that we are talking about.