When using the image export function I select .png as my preferred format which supports transparency, and is supported by Mindjet as per the following article:
http://onlinehelp.mindjet.com/help/mindmanager/82/enu/cs_bitmap_export_settings.htm
However the "Transparent Background" option is greyed out, as per the screenshot below:
The option to export with transparency as .gif works, however the user group who within my organisation that uses Mindmapper do not want to use .gif and only want to be able export as .png.