Does anyone have some tips on how to remove blotches in window panes due to polarization?

The original post title says “blotches in window panes” and I responded because I remember seeing that effect in some of my own photographs. Although I don’t know the exact reason it happens, I think the polarizer might be interacting with how window light has been modified by various coatings and layers in modern windows. For example a “low-e” window has a microscopic metallic coating that helps block sunlight, intended to lower a building’s air conditioning load without blocking your view outside. Although the coating is invisible to the human eye, it uses a metal such as silver and I’m wondering if that is what creates blotches in polarized pictures through those windows. 

So you are right, a polarizer would not normally produce blotches, but I think shooting through a window with a polarizer filter does introduce potential blotchiness depending on how the window was manufactured. And I don’t think the reflection removal tool is trained to recognize and remove those.