From the pictures, While the table top edges are solid, the center is almost certainly veneer. That's a pretty common build for Danish teak furniture. With all of the Scandinavian tables I've ever seen, the end grain shows obviously when they're solid teak.
As others have said, I'd start by stripping, including the table legs- you should be able to disassemble the table, to avoid getting stripper on the cane shelf. After stripping, I'd wipe surfaces with mineral spirits before going to oxalic acid or bleach, which might result in unintended color changes themselves. Mineral spirits will give you an idea of how your final finish will look, and whether you have any stains that will show.
With veneer, I'd be really leery of using a ROS (or any powered sander), for fear of sanding through the veneer, at least at the outset, and certainly not with coarse paper. If you do need to sand, do it by hand, using only medium to fine grits, and be careful. Most of the Teak veneers I've seen are really thin. Good luck, and post pics when you finish!