DIAGNOSIS This is a classic new-appliance taste, usually from the food-grade tubing and seals inside. It should fade, but you can speed the process along.
FIX Do a thorough cleaning cycle, but not with the official cleaner packet first. Mix a solution of one part distilled white vinegar to three parts water. Fill the tank with this, run a clean cycle, then discard the first few batches of ice. Follow that up with a cycle using just plain water to rinse. Repeat the plain water cycle if you still detect a hint of vinegar. For daily use, always use filtered or bottled water—minerals and chlorine in tap water can react with the new components and make the taste linger longer.
IF THAT DIDN'T WORK Check your water source itself. If you're using a new filter pitcher or fridge filter, sometimes those have a break-in period too. Try using a few gallons of a known-good bottled spring or distilled water to isolate the problem.
HEADS UP Never use chemical cleaners, bleach, or soap inside the water tank or system. That taste will get into the ice and is very hard to flush out. Stick to vinegar or the official GE cleaning solution.