there should be a plastic plate under the battery with a drain spout.
if you really are worried about "dust" then find a spray bottle and fill it with soap and water, lightly spray and clean off the dust. But might as well never drive the car too - as the car rolls down the road it will gather dust etc. Its pretty normal.
Use proper caution and products to clean such items, e.g. you do not want to clean aluminium engine parts with alkaline cleaners, they will corrode aluminium. The usual answer I had in Pakistan was "kuch nahi hota"
My patience runs out at that point and I automatically revert to "mute" - I dont want to argue with such people.