Hard water and soap scum can be kept at bay by using a sponge or towel soaked with lemon juice. The acidic lemon juice breaks down the dingy grey build up of soap scum/hard water stains. For build up you can use a commercial product designed for hard water stain removal, it will be a more aggressive acidic cleaner. Or a home remedy is to use cream of tarter and hydrogen peroxide to make a paste allow to dry and buff and rinse clean.
Potassium bitartrate (cream of tarter) can be mixed with an acidic liquid such as lemon juice or white vinegar to make a paste-like cleaning agent for metals such as brass, aluminum or copper, or with water for other cleaning applications such as removing light stains from porcelain.
The much easier solution is to clean the hard water/soap scum frequently so you don’t have a big tough job of scrubbing.