Start off with 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 excess oil from this process.
Now for the leaf portion of the table.
Use steel wool with teak oil and rub the area over several times- again remember to wipe off any excess oil once the leaf portion has absorbed it properly.
This process will help refine the oil buildup as well as make the leaf portion 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 practice and patience to get it just right.
Get started as soon as possible so you can enjoy the rewards!