As far as I experienced, if the Muse Sites are in a different place than they were originally, Muse asks you wether you want to drop them out of the list or not as soon as you start Muse.
That should help
Not quite clear, what you want.
- You have linked other sites on your index page? Select the link, go to the „Hyperlink“ menu in the upper control strip and click onto the „X“ icon.
- Do you want to delete a page from your site? Go to plan mode, hover over this page and a „Delete“ icon appears top right of the page. A right click onto the page leads to the same result.
And? What means „several sites on my Muse index page"? Links? Or what?
If you want to clear the welcome screen:
Click [File] > [Open Recent] > [Clear Recent]
That will clean your welcome screen.