How do I permanently delete old books in the Books app linked to iCloud?

You can delete the books that you have purchased outside of Apple's Bookstore and imported to Books and iCloud.

When I try to delete a book, that has not been purchased from Apple I can delete it from iCloud, see for example:

Just try it, but save your book somewhere else, so you do not lose it.

For items purchased from Apple's Bookstore you can just remove the download.