In RH8 I have broken links that won't restore. The message when I try to restore is the following:
The message says the topic is outside of the project folder. When I go into IE and move the file into the folder I think it should be in, I still have a broken link. I have many broken links similar to this one, the message is like the one in the image above.
How to restore topics to a project folder?
I can't really see your screenshot - it's very distorted. However, I'd guess you have a hyperlink that is pointing outside the project and you need to fix the hyperlink. (Or Index or TOC entry or Related Topics button, etc.) You should be able to click on a reference in the dialog bin your screenshot and click Edit, to take you to the problem reference (try a reference with a Topic icon first as they are usually a little simpler to deal with, IMO).
If you've already moved a lot of files outside RH, you may have complicated the issue, as if the file was actually in the correct spot, moving it will have broken all correct hyperlinks. You'll need to move them all back to the original locations if they were actually correct.