The phrase "muddy paws" usually refers to the dirty or soiled paws of animals, particularly dogs, when they have been walking or playing in muddy areas. Full definition
And before owners realize it, they end up with a large, heavy dog leaving muddy paw prints on everybody's clothes! (puppy-training-solutions.com)
And it jumped on the couch with muddy paws. (sbnation.com)
At that growth stage, dogs can easily knock over people leaving muddy paws on their suits and concerned looks on people's faces. (notinthedoghouse.com)