If you receive Windows Update error 80070003 while checking for updates, you need to remove the temporary 

files that Windows uses to identify updates for your computer. 

To remove the temporary files, stop the Windows Update service, delete the temporary update files, restart the Windows Update service, and then try to check for Windows updates again.

It's explain here

The Windows Update Troubleshooter is available that fixes some problems with Windows Update, and it might resolve this error for you.

Deleting temporary update files will help solve the problem, but it will also delete the history in Windows Update. You can still see which updates are installed on your computer by going to Installed Updates.