You can see the images your customers download from proofing events from the proofing control panel. The activity section allows you to see the number of downloads as well as the exact files downloaded by customer.
Click on a contacts name or email address from the list of contacts (or click on the number in the downloads column next to their name). Then click on downloads.
You can click on the image thumbnails to view the image larger, export the list of file names as a CSV file, or print the list of thumnails and file names.