I emailed Canon regarding the repair procedure of the affected 5D Mark III's.
This is what they replied:
"... But even for the unfixed cameras there will be a free of charge service offered at our service station to replace the light shield from 10th of may."
"According to the information I have it is a light shield between LCD-Illumination and Exposure sensor located at the prism unit."
Thanks.. I was wondering about this since their free service announcement...