You need to initialize the JQ dialog with modal set to false
Official doco on how it works is here: http://api.jqueryui.com/dialog/#option-modal
Provided that the text/fields/data to be submitted isn't huge, you should also consider jasonscript's idea of presenting the data in the popup. From what you're saying though, it's more important to show what they might have MISSED, not just what they included. Perhaps an on the fly screenshot of the webpage at the point they opened the submission form? That would show their selection clearly.