This is just my opinion, but I'd use the kitchen faucet first to flush/float that crud off. Just a modest flow of water and shake it off, then once more again, then finish with a lens wipe.
When I recently picked up a new pair of prescription glasses from Lens Crafters, that is exactly what the rep told me to do to clean the lenses.
People saying use a brush first ? yeah - that's how I always cleaned my new cars too - brush off the dirt then wash it .
Soak the lens in warm water with a mild hand/face soap lightly wash away the dirt with the microfiber cloth , then dry the lens lightly with microfiber cloth . Skip the brush and cotton .
