White plastic particles in ice

I am finding what look like white plastic particles in my ice from the ice maker inside the freezer. There is not a filter on the water line from the valve to the ice maker. It is also spilling some water down onto the ice bucket. Could it be that the ejector tines are scraping each other and starting to come apart or is it something in the water line building up like impurities? Is the water spilling over because impurities have built up in the fill spill way?