From Longman Dictionary of Contemporary Englishgrubby hands/paws/mittsgrubby hands/paws/mittsinformal used to talk about someone touching something or becoming involved in it when you do not want them to Keep your grubby paws to yourself! I bet he can’t wait to get his grubby hands on my money! → grubby
Examples from the Corpus
grubby hands/paws/mitts• The children are fighting under the tank, catching drips like diamonds in their grubby hands.• Benedict imprisoned her closer, oblivious to her grubby hands caught against the pristine whiteness of his neckcloth.• Every grubby penny I can get my grubby hands on, every grubby day of my grubby little life. 