I wrote a blog post about this before, but unfortunately, the method I showed you guys was awful and creates a bunch of pixellation. You don't want that. This method is much better.
When correcting the colors on something that's intended to be printed in black and white, you should always change your color mode to Grayscale, otherwise Curves won't be a very effective tool for getting rid of unwanted grey. Let's do this the wrong way first, so I can show you what I'm talking about.
It looks right, doesnt it? Let's zoom in...
So I change the mode to grayscale, and make my Curves corrections in that mode.
Now all that blue reads as grey.