I'm not sure why people are attributing the eye strain solely to the computer screen. [Note: this post is kind of long-winded, so skip to the last three paragraphs if you're not here for science class]
The eye strain most people are having at their computer is due to the subtle difference in frequency of their monitor and the fluorescent lights overhead.
Nerds will all know that their monitor operates at a specific frequency, and you can adjust it in your computer's settings. The native frequency is usually 60Hz (the power line transmission frequency), but some monitors have different native frequencies.
This means that your screen doesn't emit a steady light, it flashed at you so fast that you don't notice it. You can test this theory by keeping the screen in your peripheral vision and focusing on something else - most people can then see the screen flickering. It works with televisions as well, even the old tube-style ones. Ever see a video recording of a monitor or TV and it flickered or had those lines running down it? That's the same effect. The video recorder grabs the picture at a different rate of speed than the screen produces it, causing distortion.
Now, the normal person sees at about 32 frames per second. This means that the monitor flashes nearly twice as fast as you can see, and your eyes will fill in the extra with the light left over from the last flash. No harm, no foul.
The problem comes in with overhead fluorescent lighting. Those lights also flash, and it's usually at a different rate than your screen. To find out the frequency of your lights, you would have to check the ballast model's frequency and then do some back-of-the-napkin math against how old (or new, in some cases) the light itself is.
Some fluorescent lights have a frequency of 60Hz, but that's for a full cycle. That means that in the first part of a frame (1/60 of a second) it's getting brighter, and the second part of the frame it's dimming. As the tube gets old, that frequency lowers. There are a lot of different reasons for that, from the ballast to the cathode to the starter. If you're interested, you can learn more at the wikipedia page about it.
The difference in frequency between your screen and your room lighting is what causes eye strain and headaches for most people. The lights are flashing at a different speed than your screen, and even though you can't see it, your eyes are affected by it.
I never had eye strain problems at previous jobs, but I think that was because I could always turn off the overhead lights and I'd put an incandescent (or LED more recently) light in my office. Now I'm in shared workspace and I can't do that. I started getting eye strain issues around the end of the day, and I'm in for one to see if these help.
Bottom line: For $40, if they work then I've saved myself a lot of headaches. If they don't work, well, I've spent more on far worse ideas.