I assume that you are using the DX lens, as the FX 14-24 lens doesn't accept a UV filter.
At some risk of being branded a heretic, I'd say "don't worry too much about it". The anti-reflection coating is fairly tough on modern lenses. I'd be inclined to wet a cloth (ordinary water should be fine) quite thoroughly, and float the bits of glass off, using each section of cloth only once. The water is a fairly effective lubricant. Then clean and polish as usual.
On a related note, I'm not convinced that using a UV filter all of the time is a terrific idea, as it increases flare, and slightly reduces the effective lens quality a little bit. Of course, there are times, like when your daughter bashes something with the lens, that you've got to be happy that you had a filter on it!