You've got several options, none of them fun unfortunately!
Scrub scrub scrub!! or... scrape with a razor blade.... or I've heard some use stuff like vinegar. I'd recommend not using anything that you wouldn't want you in your tank though, just in case. It's up to you, but I've had to resort to using a lot of elbow grease.
I tied lemon juice after reading it from AA, it worked just do not use the half or whole lemon directly on the glass, just the juice, its seems to cut through everthink
Before you do any scraping or scrubbing, be sure you are working on a glass or metal surface. Plastic will scratch too easily and the result could be a "frosted" effect that will also block the light and which cannot be repaired.
For plastic you will probably want to use a chemical product such as Jungle's Lime Off or white vinegar. Put the whole thing under running water to rinse it completely away when you are finished. Take every precaution not to contaminate your tank.
The best way to deal with these water stains, since you are now aware that the water in your area will produce them, is to keep after them and remove them before they build up again.
I use vinegar to clean the black hood and and the silvered PLASTIC reflector on my Juwel Rekord 120.
This works fine as it is non abrasive so won't scratch the plastic reflector. Just dampen kitchen paper with the vinegar and leave it on the offending stain. GENTLY rub with the towel and it should lift off. Be sure to rinse the vinegar off. I know we like vinagr with fish (and chips) but I'm not sure they will appreciate it.
I wonder why the folks who make tank covers don't make them smooth, at least. The rough texture on mine make that annoying stuff even harder to get off!!