You clean your bathtub regularly to remove soap scum, stains and grime build up. The only stains you can't remove are the ones under the bath mat. Bath mat stains are difficult to remove because the dirt is compacted into the bathtub surface. The stains need to be treated with a cleaning paste that can penetrate the dirt and not push the stain further into the bathtub surface. Once the stain is penetrated, you can scrub it away with a pumice stone.
Mix 1 cup of baking soda and 1 cup of lemon juice in a pot. Stir the mixture into a paste using a spoon. Wear latex gloves to keep your hands from getting wet.
Scoop out the paste with a sponge or soft cloth.
Apply the paste to each bathmat stain. Rub the paste into the stains.
Let the paste dry.
Use a funnel to pour 2 cups of white vinegar into a spray bottle.
Spray the white vinegar onto the paste-covered bath mat stains. You will notice some bubbling and that is OK.
Scrub the bath mat stains with a pumice stone until the stains are gone. For stubborn stains, respray the spot and scrub with the pumice stone.
Rinse the bathtub with hot water from the shower or faucet.
Clean your bathtub regularly with the baking soda/lemon juice paste to keep dirt and soap scum from gathering too heavily under the bath mat.