How to remove (some) gmail folders in Thunderbird

You can also tell gmail itself to not present the relevant folders to the IMAP user (thunderbird) at all. To do this, go to Gmail > Settings > Labels, find the relevant labels, and untick "Show in IMAP".

Unsubscribing the "important" folder can resolve the issue.

This can be done by right-clicking any folder in the inboxes panel and clicking "Subscribe...". That will load all folders Thunderbird is currently watching, and you can untick the box to unsubscribe from "Important".

You can find further information on imap folders and subscription in this superuser quesion: What does it mean to “subscribe” to an IMAP folder?