You mention that the rain gutters have screws holding them on. This indicates that at some point in the past, a previous owner has dealt with them in some manner. The rain gutter is in two parts... a backing strip that is nailed to the top wood and the actual gutter which snaps over the backing plate. The screws are likely installed where they go through both parts. I would be afraid that if I removed the screws, the whole assembly would come off or at least come loose. If you are only concerned with appearance, mask them off and paint them.