It's pixelated, but that isn't your biggest problem.
Your biggest problem is going to be that the word "corporation" is never going to look good when the logo is that small (it may be better on a retina display). This is mainly because, even with that text being bold, it is still too light-weight to be clearly seen in that sea of black when everything is reduced down to 40px high.
I'd suggest asking for a version that basically inverts all the colors. Put "MTC" in a black box, and Corporation in black (white background) underneath it.
If you're unable to get them to alter the logo at all, you can help alleviate the issue by making it a bit bigger. Even an increase to 60px seemed to help a little to me.