Appliance Repair Wisdom for the Ages

I have a ~1986 GE side-by-side (model #TFX22ZGB, S/N VS-211967) with their standard crescent-cube icemaker. Recently the ice has developed a foul taste and odor-- it is clear with no particles, but it just stinks! I can find no filter to replace on the water line. Which filter do you recommend I install? Do I need to install it on the supply water line before the solenoid valve, or can I install it on the plastic line on the backside of the fridge between the valve and the icemaker? Thanks for your help.

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