The Magic Mouse

The Magic Mouse, or the Mouse, was a well-known patron of the I-Thou coffee shop. When Summer, Polly and Ben were there in January 1967, other denizens claimed to have seen the Mouse freak out, which "never happen[ed]". Then they claimed that he had vanished in front of their eyes. A man who had overheard the characterisation said that the Mouse's apparent demise was the result of dropping Blue Moonbeams. (PROSE: Wonderland)

Behind the scenes
Unlike most every other name dropped in Wonderland, this character does not appear to have existed in real life.