What do you mean by "photo cleanup"?
Your photos are not "in" Lightroom, the photos are on the hard drive and referenced by Lightroom.
If all you did was move folders around, you just need to tell LR where you moved them to in the Folders panel.
If you moved individual files around, you just need to tell LR where you moved them to in the Library grid view.
Importing a second time is almost always the wrong answer to every question. However, if you really want to do that, you can create a new catalog (menu /file/new ) and do an import using the "add" option. Note that this will lose all your previous photo edits.
I did all my deletions using the Mac Finder. I keep reading that you should do this sort of thing using the Lightroom catalog, or else you'll get lots of Lightroom previews bearing exclamation marks, which require you to find the photo and relink it. I'll go with your suggestions. Thanks.