I think that's where I'd start. It might be good to try to determine what sort of oil is on the table; the scent might be helpful. And, try just a tiny area first, to judge the result.
If the wood is lighter where the mats were, that's a separate issue. In my experience cherry is very photosensitive; raw wood can darken in a couple of hours when exposed to direct or indirect sunlight.
A solution is to mask all of the darker areas, and expose the lighter wood to UV. Trial and error is the only way to proceed, there.
Thanks. We'd hate to lose you, Leif. I've been enjoying the old-timers and neglecting the rest of the site. Guess it's my tiny substitute for facebook . . .
I'm told that the site was sold in February, and so it's a relief to see that nothing has changed. You don't value something precious until it disappears ?
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