I'm hardly a water cooler but I've worked with copper all my life.
Looks exactly like the various stages of slightly acidic water + oxygen over time. Like if you left raw copper outside without touching it. Looks perfectly normal to me and you should easily be able to remove most of it with something slightly abrasive (textured sponge thing) or viperous scrubbing with cloth. If it is just oxidized (the way that copper gets dark when it remains dry) you'll need to lightly scrub with something a bit more aggressive like scotchbrite. If you tear a piece off you can push it in the gap there and use a pencil or something to push it around. Or use the corner. No matter what it is, one of those the answer (if you want to remove it).
Ketchup and a toothbrush is also very good for copper (but don't use it on nickel)
I wouldn't believe it if I hadn't done it myself. Ketchup really is the best product you can use for cleaning something down to bare copper, even better than products designed to clean copper. Fast too.