Covering a TV behind your speakers?

I’ve heard a couple of folks say the audio sound field is in front of the TV, thus no effect, so no worry about reflections from the TV behind it.

How, exactly, does that theory work with my MMGs? Or any other bipolar speaker that radiates sound from the front AND the back, especially when they're 3-4' out from the wall the television shares?

For the record, I had a bit of material left over on a roll of landscaping geofabric. It’s black, so blends in nicely. I cut a small roll of it to a width just past each edge of the flat-screen television and long enough to hang just below the bottom edge. I unroll it and hang it off the top (had the wife sew a narrow "quiver" or slot in the top that I slid a wooden dowel into. Still light, but heavy enough to anchor the piece to the top of the television. When I want to listen critically, I pull it out, unroll it over the television, and enjoy. I can say it certainly doesn’t HURT my soundstage depth/width, and seems to my ear to deliver a bigger difference with well-recorded and mixed music like Steely Dan. It always sounds quite good to begin with, but pulling down the veil over the television kind of serves as a cherry on top when listening hard.

A sound absorbing panel that covers our flatscreen tv improves the sound of my system. Haven’t tried a diffuser panel.
I use a commercial acoustic panel leaning at a slight angle in front of our 42” tv, during a listening session; and remove it to a space between the wall and a small cabinet when not in use. 
The tv sits on top of an open -shelf component stand approx 24” high; Magnepan speakers positioned in a plane 24” in front of the tv.

Okay, after reading this article I gave the blanket over a 65" tv setting atop a stand behind the speaker a shot. I had a relatively thick blanket to use...and sure enough, there’s a much better soundstage than before. I didn’t believe it would make much of a difference, but it does. A hearty thank you to the AG crowd chiming in!

I too, have found benefits to putting a highly textured throw over my TV for serious listening. Free to try...

I also refuse to have a screen between my speakers.  I do use GIK diffusers and have 4 of them behind and between the speakers. Sound stage is incredible.

Occasionally I do watch TV off to the side as a visual background to music. 

Ideally I would like to have the screen between the speakers. 
I would do it if they made a screen with convex curvature.