The table actually had white marks when we got it. The lady we bought it from said that was why she was selling it. I didn't mind because I was already planning on refinishing it anyway. We got the table and chairs for $125. Bargain!
The white marks you see here have arrived over a long period of time. I get to the point where I hate looking at them and then I do the magic trick! I found this idea way back when on Pinterest and it has worked each time.