I assume the problem is that the water is hard and this is lime scale (Kalk).

I'm not sure a filter will make a blind bit of difference. There are 3 alternatives:

1) A water softener. This requires salt and back washing etc. and the permission of the owners if you are not. The water will then taste awful and soap will be virtually impossible to get of your skin.

2) A semi hockus-pockus electronic system, which changes the scale particals' electric charge for about 12 hours and theoretically means they can't hang on to anything (like your kettle) until their charge reverts. Works a bit. But not enough to warrant the CHF1500 Price tag.

3) A full hockus-pockus magnet system. The cheapest - but doesn't work at all.