The background images themselves can be downloaded using the API.
As an example, for this experiment:
http://connectivity.brain-map.org/projection/experiment/cortical_map/543679575
You can get information about the file with this API call:
http://connectivity.brain-map.org/api/v2/data/WellKnownFile/query.json?wrap=true&criteria=%5Bwell_known_file_type_id$in501029518],[attachable_id$eq543679575]
Replace the id 543679575 with other experiment ids if needed.
In the JSON that is returned, precede the ‘download_link’ value with ‘http://api.brain-map.org’ to get a URL that will download the PNG image to your computer.
So, for this example the full download URL is http://api.brain-map.org/api/v2/well_known_file_download/550319947