The background color is conveyed via the PNG "bKGD" chunk.
From the command line, you can use "pngcheck -v". Download and install pngcheck from
pngcheck -v file.png
If a bKGD chunk is present in the PNG file, pngcheck's output will include something like this:
chunk bKGD at offset 0x000a0, length 6
red = 0x00e0, green = 0x00e0, blue = 0x0080
You probably already have ImageMagick (version 6.6.9 or later), so you could also obtain bKGD chunk information, along with a lot of other stuff, by typing
identify -verbose file.png
and look for
Background color: srgba(224,224,128,1)
png:bKGD: chunk was found (see Background color, above)
If only "Background color" appears but not "png:bKGD:...", then identify is reporting ImageMagick's default background color and no bKGD chunk is present in the PNG file.