How can I make logo background go away?

I have a logo I am trying to use on a promotional item, but I am having a hard time. It is a black drawing with a white background and I am trying to put it on a dark gray pamphlet.

Inverting the colors doesn’t work because when the background is black it is darker than the page it is on, which looks almost as bad as having the white.

Changing the color of the drawing and getting rid of the white square surrounding it would be perfect, but I can’t do it. Inverting the colors and getting rid of the black square would work, but I can’t do it. All I have to work with are Paint and Word – yeah, not great.