Stuff in ice

Hello,
I have been finding stuff in my drinks at home after the ice melts? Sometimes its pieces of plastic that are clear chunks, as if some part is flaking off. Other times its a white chalky substance? I’m not sure what is happening and am considering replacing the ice maker. Do have any idea what’s wrong?
I realize the "white" powdery-looking substance is most likely a buildup from the city water over time. Could I just remove the icemaker and take something apart and clean it?

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