The main purpose of the carbide die is to eliminate the need for resizing lubricant which is needed with regular steel dies. However, I have heard others on this forum mention using lube in conjunction with carbide dies.
Speaking for myself, with straight-walled pistol/revolver cases, i.e. .38 Special, .357 Magnum, 9 m/m, .45 Auto, & .41 Magnum, I have never had the need to apply lubricant when utilizing carbide resizer dies. I do make certain to tumble/clean the cases to eliminate scoring and to minimize wear on the carbide insert.
Others may know more though. Good Luck!
JPJ
P.S. I approached this post from the standpoint it was a question on "lube". If you were merely asking how to clean your die, my apologies for rambling on. Post 2 provided good info. For cleaning per se, I just use a Q-Tip with Hoppe's Solvent to pick up any debris.