You can't remove an app from Launchpad if it hasn't been installed from the Mac App Store. Unfortunately, you can't change it, but there's a trick.
What you can do is to download an app from the Mac App Store. Then, go to Applications folder, right-click the app and choose "Show Package Content". Then, go to Contents folder and copy the folders related to the Mac App Store to the app you want to delete from Launchpad (you have to access choosing "Show Package Content"). However, note that this only removes the app from Applications folder, so it's better to do it manually from Finder
Curious: wouldn't simply dragging the app from the Applications folder to the trash (or using its uninstaller) also remove it from the Launchpad once you restart/boot up? That appears to be a lot easier. I prefer not to use Launchpad - do all my installs/uninstalls via Finder/Applications folder (I have absolutely no apps purchased at the app store).