In an attempt to try and organize my pictures I moved them into one folder LR4 using LR to do this. It also helped eliminate duplicates. But what it also did was I forgot I had the logo checked. So every picture whether it is mine or not has my logo. Is there a way to back out of this or to remove the logo? Thank you.
Moving should not have been able to take any action like adding a logo. Export (and reimport) has this ability.
Applying a watermark is available only when doing Export, Print, Web or Slideshow creation. Could you have possibly Exported, then Imported, rather than moved?
Assuming you didn't Export and Import, select an image with the logo, go to Develop module and look at the History on the left hand side. You should be able to 'go back' to a time when the image did not have the logo, though frankly, applying a logo in Develop is not a feature of Lightroom.