The first step is to identify what kind of finish os on the table.

Lacquer can sometimes be repaired by simply applying another coat of lacquer.

There's a scant possibility that the white is just in the very upper reaches of the finish and can be buffed out with rubbing compound, then waxed. Some people swear by toothpaste for this, but I use a auto body swirl mark remover. You'd have to polish the entire top to get it to have the fame sheen.
Casey

I use these (professionally) and have never had a problem removing a water blush in just a few minutes. You can also usually find them at Ace Hardware, Lowe's and Bed, Bath & Beyond in their cleaning / furniture care product aisle.

In my experience, rarely would you need to strip and refinish unless the finish is blistered and peeling off (I can't tell from the photo)

Likewise, you may need to buff out the whole top to even the sheen. The cloth will also remove light scuffing. Clean up the residual oil with an emulsion furniture polish

Here is a link that might be useful: water ring removal cloth