CLR will do a good job on lime-I recommend wire brushing first and then apply the CLR with a cheapo paint brush. You did not state the thickness of the buildup. Lime usually will brush off for the most part. If there is a heavy buildup, and upon removal, you find the fittings beneath "wasting" away then you probably have an electrolysis issue.
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Wm. F. Buckley, Jr.