When you absolutely, positively, emphatically cannot have any glare, or specular reflections, we need to break out the science. You can think of light as acting as a wave, vibrating in any direction. If you pass light through a polarized filter, that sheet will only allow through light that is vibrating in a particular direction. For instance, if it is a vertical polarizing filter, only vertically vibrating light will pass through the filter and the rest will be filtered out.
Having a single polarized filter will not actually immediately fix the problem though, it ensures just that all the light hitting our artwork is vibrating in the same direction, but does hold the key to fixing our issue! Diffused reflections will change the angle of the light waves again, so they could be vibrating in any direction after they reflect off the surface. Specular reflections (glare), on the other hand, will maintain the vibration angle of the polarized light, in this case: vertically.
As we don’t want that glare, we can use a second polarizing filter, this time set horizontally, to filter out all the vertically-vibrating specular reflections, leaving only the diffused reflected light that is vibrating horizontally. This will completely eliminate all the specular reflections, leaving you with a nice, glare-free image.