The white mark is caused by the boorish diner's hot tray causing a separation between the wood and the finish.
As has already been alluded to, try using a white, clean cotton fabric, such as a dinner napkin or the proverbial T-shirt and a steam iron. Place the cotton fabric over the stained area and then use the iron in "non-steam" mode for about a minute or two with a moderate heat setting, as if ironing the fabric... then when the wood is thoroughly heated, use a burst or two of steam and continue ironing until mark is gone.
What you're doing is acutally removing the whitish area from between the wood and the finish. It's worked well for me on several occasions (boors here in the U.S. too), although there was one older oak table that had been finished with a homemade concotion way in the past on which it simply would not work ... wound up refinishing the piece...