How do I get what I think are water spray marks off my furniture?

I have what turns out to be very expensive LAMINATED wood furniture. You are not supposed to clean it with anything but a damp cloth but I noticed this morning that there was what I think is a water spray mark on the front of my dresser (probably from keeping the dogs in line with a water bottle!). I can't get it off with just a damp cloth. Anyone have any ideas of what would work on a laminated piece of furniture?

Thanks in advance everyone!