I'd honestly re-draw it in illustrator. If you try to use the magic wand, you'll pick up the white in the half tone. Also the resolution is crap, I would find this artwork almost unuseable, unless I was shrinking it to say an eighth of it's size, but even then.....
Sorry chap, you would get far better results with spending a little time drawing it in vector, it's not that complicated, especially if you have the font or similar to edit. You may also be able to charge for cleaning up their logo.