It seems as if there is some anti reflection coating and that doesn't seem to be very hard
Canon saved some $$$ buy just putting a plastic lcd into the 6d, the 5d3 has a glass cover ... so the very first thing after buying is to stick a protective plastic cover on it or order a glass protector, ebay/China for €5...
... but don't dispair, if you put a non-reflective cover on it now the scratch won't be as visible as now.
Now that you mention it!
Damn, didn't realize this before.
Do you have a recommendation for the protector? I found this one here made of glass: