Thanks everyone for your thoughts about whether I should paint my thrifted game table or not, and suggestions for getting rid of the large iron shaped heat mark marring the top.
I did buy some Old English Scratch Cover (thanks Cheryl!!) and it helped, the tabletop looked better in general, and the scratches were less noticeable... but the white spot was still there.
The day after I posted about the table, a small package from Amazon showed up on my doorstep. My daughter E had seem my post, found the wipes she used to use for white spots and ordered me a package.
Wow, what a difference. The wipes seemed to fade the white spot... It's still there, and in certain light you can definitely see a difference in the wood in that spot, but it's obvious only if you're looking for it.
Here is a before and after:
Before... a glaring white iron shaped mark!
And after... it's hard to see the spot that was so white before, it's almost faded away... (I can see I need to work more on the other round heat mark... with the big mark almost gone, it's suddenly really noticeable.)
And here's the furniture wipe E got for me (Thank you so much E, I'd been looking for these, what a very nice surprise!!)
So... at least for now... the table will remain "natural". I'd rather not paint it, it's such good wood, and E says the more I use the furniture wipe the more that spot will fade away...
I love it when something I thought would be a big job turns out to be quick and easy!