Your pump filter should catch the rest of the dust. I clean mine in a spaghetti strainer.
You need to worry more about stabilizing its pH.
Soak it in water that is pH'd to 5.5 and watch as the pH rises over the next few hours! I use a aerator during this process to more closely simulate my res conditions. Keep adding pH down until it STAYS at 5.5-6 for 24 hours, then rinse well with fresh water. Now it's ready to use. Keep a close eye on pH until you're certain that it is stable.