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There is a label on it: POM

FYI, POM is the plastics industry name for Acetal (Polyoxymethylene) and has no purpose for part identification. Just like you'll see plastic bottles with PP (polypropylene), or PE (polyethelene) on them.

 

[Shiro_se]

I replaced all the belt trim molding on my 2005 Mazda6 in around 2010-11 for around $200CND. It might surprise you how affordable the entire piece might be at the dealer.

Also, if you're worried about water getting inside the door, they are hardly waterproof. That trim mostly keeps large debris and sand out of the door cavity. Water can flow right past the flocked, soft material that rides on the glass. The doors have drains in the lower edge to prevent water accumulation.

Alternatively, if you don't want to replace the trim, use some dabs of strong adhesive to hold it in place. Something like Automotive Weather Strip Adhesive, E6000, etc. Use masking tape to hold it in place until the adhesive cures.