I think I agree with Craig, I just maybe have a different way of saying it. I see it as end grain of figured areas coming to the surface. I would guess most on this forum have more experience with this, than I, but I would work down the dry finish in the big middle areas with fine steel wool( maybe 00), but next to inletting and corners with fine abrasive paper( 400-600 grit), backed up with a rubber/wood/or hard felt block. Take the surface all the way to the wood. The reflective areas are where the grain is filled and there is finish on top of the wood. If you look closely at the dull areas, it looks like the grain is not quite filled( the end grain will take in more finish than side grain). You can concentrate on the dull areas by applying finish, take it down, do it again until all the dull areas are filled. Once this is done take the whole surface down to the wood completely. You will then have the finish in the wood, rather than on the wood. At this point, you can apply whatever finish you want and knock it back to suit yourself by what ever way you prefer. What I like to do for the final finish in to rub in one coat of "Boiled Linseed Oil". Then, when( not if)I get some rain spots or other small defect from use, I only have to rub it up with fine steel wool and rub in another coat of oil.
There will be disagreement with my method, some likely very forceful, just remember I already admitted everyone else has more experience than I.
Mike