Over my lifetime, I've owned quite a few dogs. I'm old. Anyway, among the dogs I've owned, I had a poodle. If the poodle went out in the morning, and there was dew on the grass, or it had rained so the grass was wet, we had to faithfully dry the dog's feet, in between the toes, both on the top, and bottom. If we didn't, the dog would get a sort of foot fungus. At first, there would be no visible signs, but the dog would go crazy licking his feet. Back then there weren't that many antifungal, athletes foot type products, so my mother suggested merthiolate. WARNING: DO NOT put merthiolate on an open sore, because it burns like fire. All I know is, it worked. At the first sign of the dog constantly licking his feet, we would put a bit of merthiolate on them, and it would clear everything up. Now, I suspect at least one of the athlete's foot creams, or sprays would work just fine.
He was the only dog I ever had that was like that, but his feet were sensitive to wet grass his entire 16 years of life. This may not be your situation, but then again, it could be.