E. Cobham Brewer 18101897. Dictionary of Phrase and Fable. 1898.
means the foot of an animal armed with claws; a hand. To claw is to lay ones hands upon things. It also means to tickle with the hand; hence to please or flatter, puff or praise. (Anglo-Saxon, clawu, a claw, with the verb clawian, to claw.)
Claw me and I will claw thee, means, praise me, and I will praise you, or, scratch my back, and I will do the same for you.
Laugh when I am merry, and claw no man in his humour.Shakespeare: Much Ado, etc., i. 3.