Cleaning Refrigerator Lines and Water Reservoir?

You can follow these steps for clean your refrigerator water line:

First you must turn off your water supply to the cooling system.
Pour some distilled Vinegar into a cup and pour it down the tube. (If your fridge has an ice maker as well, turn it on so that the vinegar will clean the ice maker system as well)
Try to get a bottle brush to dip the end in the vinegar this way you can clean inside the water sprout as well.
After you flush your system out with vinegar make sure to turn back on the water supply and let it run until you can see that there is no more vinegar in the system

You can pour a glass of water to see if there are any leftover remains of the vinegar.
Also, if you do have an ice maker, be sure to throw the first 2-3 batches of ice out after this process because they will most likely have vinegar in them.
Just to make sure there is no excess vinegar in the ice tray, you should take out the tray and soak it with warm soapy water. After you soak it, its important for you to rinse it thoroughly. You want to rinse it as much as possible with hot and clean water