Your new fridge most likely has a water filter inside.
Add an "in line" filter on the supply line, replace them on a regular basis and your water will be odor free.

Talking about water for ice makers: I just read that most restaurants ice is full of bacteria and other crap, due to dirty filters, machines, dispensers and other reasons. Maybe not to the point to make you sick, but next time, think twice before you take ice from the filthy dispenser at your neighborhood fast food joint.