Chalk dust collects around pockets and along common shot paths. Rubbing it with a wet sponge drives particles into the fibres, so start with a dry, low-friction method.
Recommended sequence
Remove balls and accessories. Brush gently with the nap from the centre toward the rails. If the cloth maker permits it, use a cloth attachment on the lowest vacuum setting and avoid pressing the nozzle down.
Avoidable damage
General cleaners, bleach, steam, and stiff brushes can fade the cloth or lift its nap. Blot a spill rather than rubbing it, and only use a product approved for that cloth type.
Prevent repeat marks
Keep the tip clean and never shake chalk over the table. If a mark remains after dry cleaning, ask a recovering specialist to assess it; aggressive household chemistry can make a local stain permanent.