It's to do with the way the image is printed on the paper itself, not the paper. If you look at it closely, you'll see the colour is made out of an almost repeating pattern (I guess would be one way of describing it) due to how the colours are printed on top of each other to make them mix - you'll see each different colour ink of cyam/magenta/yellow/black traverses the paper at a different angle. This is what causes it to be awkward to scan.

I don't know the details to remove the effect, which I think is called Moiré, but there should be an option to demoiré a picture in your scanning program, or at least in a paint program after scanning. Can't really help much more beyon that other than tell you to try experimenting with different scanning options