OOOHHHH....He actually has dirty feet and or dirt stained feet, not urine stained feet. (much more common and I didn't know he played outside), so in that case, you can prevent further dirt staining by taking a damp wash cloth and wiping his feet after he plays. Use a dry paper towel, or cloth to dry. Of course be careful to have him secured as a bunny's feet can be sensitive, and a rabbit can kick out and injure themselves (even break their own back from kicking)
For now, if his feet are really dirty, you can do some spot cleaning with mild bunny shampoo, and it may help get rid of the brown, but dirt can stain too. Doesn't mean that your rabbit is dirty of course, just that it will need to fade out on it's own. Be sure when you use shampoo to thoroughly rinse so your rabbit doesn't digest it.
As far as what kind of shampoo, rabbit skin is extremely sensitive. Even shampoo meant for human babies can be too harsh. So you need to find one that is mild enough. I have to spot clean my bunny Bailey often, and so the vet gave me one specifically her problem. (she has a crooked spine, so I have to help keep her bum clean of urine & poo.)
There are shampoos that are meant for bunnies. You can call and see if your vet recommends one for rabbits I've read that Hy-Lyte is good. I use a similar product from that same brand but it is meant for poop cleaning. You don't need that.
I wouldn't recommend using shampoo on his feet every single time, just to get out the really dirty stuff, but if you can just wipe it off with a damp cloth that would be better for his skin.
Anyone else have some safe cleaning tips to offer?
This has sort of been an ongoing question over the years, and since bathing is not recommended in general, it's not a subject that has tons of information. I will ask my vet and other rabbit savvy people what they also recommend for spot cleaning dirt.