That's awful, I'd be in distress too! Maybe do a Google search and see what you can find out. Like linelle suggested, do you see what looks like a waxy residue or are they white scorch marks?

If it is wax from the paper use some paint thinner.

If it is a heat mark into the finish it may fade.

two words: wire racks.

If it's wax which sounds likely
Two options - brown paper and an iron on mild heat-
or benzene (or lighter fluid)
can be a little tricky depending on how deep into the wood but I'd expect not that far unless you burned the cookies.
Likely will wear off too.
Then get a better sealer and as noted wire racks make for better cookies.

Should have been clearer- put down brown paper, then run the iron over it- not too hot or long- pick up and see if you won

I've heard that Howard Restor-a-Finish is a good product. It removes heat and water marks.

http://www.howardproducts.com/prod-restor-a-finish.php

If it is wax residue, I've used a paper towel & warm iron similar to jakuvall's recommendation. Paper towel soaked up the wax great.

hth

So MIssyV, what worked? I just did the same thing :(

thatsarahwheeler, that poster has not posted in 4 years.

Try a Magic Eraser.

I used my iron on the "wool" setting for about 10 seconds (for each cookie's spot) and a paper towel, then rubbed really hard. I probably got up 95% of the marks (and the rest is because of the grain of the wood table).