What is the function of the metal mesh in the rubber grommet for the showerhead?
Yes, you are correct. The mesh is there to collect the larger sediment. I would still use it as the pipes could still have sediment and build up and possibly rust, that could pass onto the shower, even in a filtered water system. Extra precautions!!! It doesn't hurt to use it. The rubber part also acts as a gasket/seal. No water leak...or less of one!