Picasa is a cloud based service, so they should not be. You can check in settings, storage, and look at your picture/video space just to double check. You can also go to settings, accounts, and uncheck the syncing of Picasa pics. It won't get rid of what is there, but won't add any more.
Edit:-) : If they are really bugging you, remove Google account, reinstall and quickly do step above, and uncheck syncing.