It appears you are talking about going to a layout part and going to the inspector, clicking on the Appearance Tab, and changing the fill to a graphic. Once the graphic is in the part, you cannot export it. However, you could duplicate the layout and erase everything in front of the layout, then do an image capture (screen shot) to capture the image. Then you can save it on your computer and when you go to the layout you want, you can go through the same process of selecting the image to import into the new layout.
Alternatively, you can create your new report by duplicating the layout with the graphic and bring all the fields in that you want to use for the new layout/report. Basically, just start from the layout you like and modify it accordingly.
Yes, I ended up with the screenshot route, thanks. I guess I need to try and keep a library of background images for future use...