Soldato
Polish with toothpaste or a very mild abrasive like AG SRP - it will likely improve it to some degree, but as others have said only real option is to replace.
Polishing textured interior plastic with a mild filler polish?! Definitely do not do this! You'll never get the white polish out. It's bad enough when you touch exterior plastics with polish let alone working it into soft textured interior plastics.