How to remove water marks from toilet bowls

The toilet bowls in our house have these greyish streaks whick mark where the water flows in from the cistern. I don't seem able to get rid of them. In summer it's ok for me to don rubber gloves and hand scrub, but in winter it is very daunting to plunge my hand into the icy water. Is there a good way to get rid of those streaks?
Ada
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scribbled in red crayon:

periodically myself.
~Piper~ Life is simpler when you plow around the stumps.
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wrote:

to work overnight would do the job or how about a long handle with a pumice stone attached?
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