I don't know about Maya but in 3dsmax it has a similar system where you can drag the cropping methods around over the texture. It's not very accurate at all for lower resolutions, which causes seams like that. The problem is that when you drag around the lines and such in the tool they provide it doesn't round it off or anything like that, giving you very large floating values, which is bad for low-resolution textures since it has a huge effect, as you can see. The values need to be very clean.
If you can, input the numbers manually, it's a lot of work which requires minimal math and a calculate, but will crop off that stuff perfectly. What it wants is a multiplier value, a value from 0-1 which basically represents 0-100%.
You can find these values by dividing some variable values by the total width(or height) of the image. So say you want to find the U value(the position to start cropping horizontally) of your texture cropping. So if you have a texture image with a size of 128x128 pixels, and you want it to start cropping at 16 horizontally, you divide 16/128=0.125. 0.125 is your U value. For getting the W(width) value of the cropping, simply take the width of the crop you want and divide it again, by the image width. So if you want to crop out a 32pixel width, 32/128=0.25. This applies to the V and H as well by substituting with vertical and height values.
So for example, in your texture the values you'd want to input for the top-left texture is:
U: 0
V: 0
W: .5
H: .5
For the top-right it would be:
U: .5
V: 0
W: .5
H: .5
However, I am kind of a novice at 3D work. This is what I learned when I was working with Minecraft mob textures and it's the method I used. I also use 3DS Max so it may not be the same in Maya. Someone more experienced may point out my flaws but if I'm teaching a crude method I hope they do. My methods may just be arising from the poor method in 3DS max, and Maya may support it much better and easily allow you to snap to cleaner values with a hotkey or something(3DS doesn't even let you zoom in, so that just makes it all the more harder).