Odd tasting ice?

I have a reverse osmosis water filter which feeds the water
dispenser and ice maker for my fridge. Recently I noticed that
my ice has a slight ice-tea kind of flavor, or possibly a slightly metallic
taste. The water from the fridge's water dispenser is fine, so I don't
think the RO unit is the problem. I've had the RO unit about 5 years;
it's plumbed to the fridge via plastic tubing threaded through copper
pipe.

I'm looking for suggestions on what could be causing the odd taste
to the ice. I've tossed all the old ice and washed the ice holder/
dispenser tray with soap, and fully drained the RO unit, but the fresh
ice has the same flavor. I'm pretty sure it's not picking up food odors
as the taste appears immediately and the freezer is pretty clean and
uncluttered.

Thanks for any advice.

--Neil