Hi and welcome.
Crikey you must like the heaters where you are!
Never seen that before, but there is no repair other than removing, stripping, priming painting and lacquering - and to be honest that would not be worth the cost and time. Getting the oil and contamination removed is a huge problem and it probably won't look great.
However you can purchase the air vents separately that are the louvre and the wrinkled bit in your photo, which slot into the surround. They are available for the Centre and the ends.
Then I'd suggest you put 4 knitted jumpers on instead and turn the vehicle heating down!
