I have done some testing and investigating on this and I can confirm your results. In IE8 this option to edit the link does not work properly, it will not load the value or the controls needed to update the value.
When I was looking for more info about this I found that this is a known bug in the version of FCK editor that iRite uses. In the bug report it is mentioned that the issue has been fixed, it looks like the latest version has the fix. It should be worth updating the FCK editor files in your site. Here is some info on how to do that:
Before updating, I would strongly recommend backing up the WA_iRite folder. Also note that we have not tested iRite with any newer version of the FCKEditor, so we will not be able to support it.
In the WA_iRite folder, there is a folder called "editor", replace this with the "editor" folder in the FCKEditor package download.
Any other files that are at the root of the WA_iRite folder that do not begin with WA should be replaced with the new ones from the FCKEditor download. It is important to make sure you do not replace files that begin with WA.
Keep in mind, that if you update the FCKEditor, you may cause other problems. Also, if you add the functionality for Image Upload, you will need to redo the steps for enabling it.
You can also update the source files for the extension so that you do not have to manually update the files in the site when you use the tool again. Here is a link to the thread that discusses updating the source files for the extension.