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I'd test a little bit first before you go sploshing osmo all over. It looks to me (from the photos at least) to be more of a matte lacquer finish if so a hard wax repair kit would sort it. It's something I keep in my van for instances like this; fuck ups happen no matter how careful you or people you employ are. The best thing is that it's made to match natural wood tones and it's actually easier to repair wood grain than solid colours as small descrepancies in colour are hidden by the natural variation in the the wood grain.
This is a pretty good guide as to how to use the kit.
Nice one! Do I need to stain it too or is the oil itself tinted? Cheers!