How do I clean dirt off his claws?

I was playing with Puppy's feet, and I noticed that his back claws are filthy, particularly at the base of the claw. They're caked with grime.

How should I clean them? I thought about scrubbing with a clean toothbrush and water, but that's probably not too comfortable.

I would think a soft tooth brush would work well. I use one under my fingernails after working outside and it sure feels alot better then a nail brush.

All I do is use my nails to scratch it off. Easy.