Assuming it's an older teak table, use teak oil for the refining method. Start off utilizing a 0000 steel wool on the top of the table which are a bit lighter than others and clean it thoroughly. Particularly pay attention to the grey areas on the table because they are the portions that will require the most refining as they've been all dried up.
Afterwards make sure to clean the top portion of the table and apply teak oil generously. Do this several cycles in a row over the course of an hour or so until the wood absorbs all the oil. Finally you can wipe off the residual oil from this system.
Now for the leaf side of the table. Use steel wool with teak oil and rub the area over many times- again bring to mind to wipe off any residual oil once the leaf side has absorbed it properly. This process will help refine the oil buildup as well as make the leaf half seem brighter. After a few times of repeating this process over the next weeks, months, and years, it will even out more and more. This takes trial and error and patience to get it just right.
