It sure looks transparent to me in the pic you attached. I don't see any colouring over the objects in the selected area.
.......
Okay, I did it again and zoomed in tighter and if I look at the edges of the rectangle and squint really really hard I can just barely discern that the rectangle is ever so slightly lighter in colour than the background of the rest of the map. So, I guess it is "white". But the background also looks white to me. Just a slightly darker white.
Thing is, there is no discolouration of any of the roads, features, names or other objects. So for printing purposes it looks like it should be exactly as good as transparent when it's printed, and that's what this was about.
Here's an image with the avoid area rectangle filled with "white" as I suggested, and without the avoid area selected. Can anyone actually see where the avoid area rectangle is? For printing, does it matter?
........
Okay, I also printed it just to see. Guess what, it's actually better if you use white fill colour. The areas outside the avoid area rectangle have a sort of greeny-blue shading to the background. The area inside the avoid area rectangle has no background shading so all of the objects (roads, names, rivers, whatever) are just as clear as can be and easier to read.
Hey bungy, give it a try on paper. I think you'll like the result.
...ken...
P.S. An apology regarding my naming of colours. Hey, I'm a guy. We're not supposed to know anything more than the primary colours. And we mostly can't distinguish all those subtle shades even if we knew what to call them.