I played around with it a bit in Photoshop. Does this help?

That the text reads "[U]NITED STATE[S]" is pretty clear to me overall despite the fact that certain letters are mangled. And I do see the ball ornaments that Jerry referred to above the lettering, and a couple below it in the region of "ED"
So it does appear to be an offset transfer from a six cent. Perhaps one that was stuck to the reverse for a while, possibly by the residual of gum on the back of the three cent? Sometimes when that happens and the gum dissolves away the transfer stain remains.
[To get this expanded image required increasing the res to 600 dpi, then doing a horizontal flip and rotating the image 15 degrees clockwise. Using a low level sharpen filter and cropping got us what you see here.]