Dissolved Mn has to be ...

Dissolved Mn has to be converted to the oxidized state of Mn02. This requires either the use of chemicals (permanganate or some other oxidant) or raising the pH very high in the presence of dissolved oxygen (again you need a chemical) You can you pyrolusite (solid Mn02 as a catalyst) or greensand (substrate coated with Mn02) but the surface oxidation state will become exhausted and it will need some sort of period regeneration. No matter what you do it will involve some sort of chemistry. Mn can be challenging and is often "fussy" to remove. 

If your Mn is not coming out on fresh greensand (is in a regenerated state) then the contact time is too low (slow down the flow through the material) or the Mn is complexed with some sort of organic or chelating agent (ammonia for example). 

You may not find a solution without adding some sort chemical.