How do I get the black mould stains out of a tanalised treated deck?

If it is just mould or algae on the surface that is causing the discolouration you can use a 1:4 solution of household chlorine bleach and water, adding a teaspoon of dishwashing detergent per ten litres. It is important that the detergent does not have ammonia in it.

This is sprayed on and may require some light scrubbing to remove the mould. It needs to be rinsed with fresh water afterwards.

It is probably simpler to buy one of the proprietary products available from hardware outlets such as “deck scrub”, “30 seconds”, “wet and forget” or similar.