If this is a Gmail account, that setting is within Gmail, not Thunderbird.

Yes, david, my TB is linked to Gmail. I have checked the Gmail settings and I can't find one dealing with Important. Can you suggest which one?

I'm no Gmail expert, but you can set that individually on Gmail. However, Gmail does not create duplicates, only multiple pointers. My suggestion to you is to unsubscribe from the Important folder, as it doesn't accomplish appear to be accomplishing anything for you.