Dweezil and Ahmet Zappa did a version of this on Dweezil's album "Automatic". Ahmet does an uncanny impersonation of Thurl Ravenscroft, almost identical to the original. Dweezil plays a purely guitar-based arrangement of the theme (pointing out in the liner notes that there are no keyboards or samples anywhere on the track), and sings a bridge of his own composition:

I know
the Grinch, he stole Christmas, 'cause his
heart was
three sizes too small
Dweezil commented in an interview that the recording was intended to be a part of a larger "Zappa Family Christmas" project. One shudders to think.