The movie features the Jabberwocky, a monstrous, fearsome creature from the poem "Jabberwocky" by Lewis Carroll. It is a large, dragon-like creature and is not white, nor does it scratch Alice's arm.
The Cheshire Cat is a white creature, but it's well-known for its ability to vanish and reappear, not for physical contact.
It's possible you might be remembering a different detail from the movie, or perhaps a different adaptation of Alice in Wonderland. Would you like to provide more context or information?