I have tried numerous methods to rid books of mildew or the mildew smell (to me they are one and the same but others might argue that a smell of mildew or mold doesn't mean the book has it, but somehow it just smells like it from being around other items with mildew).
I have been told that X method definately rids the books of the smell.
After years of dealing with this I have come to the conclusion that none of it works.
I live in New England which has humid air and different seasons. I have come to the conclusion that some who claim to have permanently rid their books of mildew smells may have been helped by the dry climate they live in. For example a person from Arizona buys a used book from a humid location (via internet sales or other used book vendors) then they do X to rid the smell and it goes away and stays away. I believe what is really happening is the very dry climate has the mildew dormant and the method they used put the mildew into dormancy or the spray they put on it masked the smell. If that same book was put in a humid locale then the mildew would reactivate and come alive and smell again.
Adding scents via chemical sprays to books may mask the odor but it doesn't necessarily kill the mildew or stop the smell, it just covers it with a more powerful smell. I have purchased used books that reeked of Febreze but over time that scent disappeared and the smell of mildew was present. That is one trick of eBay sellers that turned me off to Internet sales of books especially on eBay, because a book seller can spray a book and make it smell like the chemical smell (I won't say "nice scent"), and then they sell it saying it has no mildew or mold smell, when it arrives it reeks of Febreze.
Another thing that has happened to me is after confirming with used booksellers that a book has no odor it arrives with a strong scent of mold or mildew and the book seller claims "I didn't smell it". If they don't smell it, something is wrong with their olfactory system or they are just plain lying.
The cat litter method, immersing a book in clean non-clumping cat litter is said to work. I have done it and it did seem to work in the short term, but a year later or more, the book reeks again like it did before the cat litter technique. I had thought the cat litter drew the moisture out of the book, it may, but over time the book sucks up the water from the surrounding air (in humid climates) and then it is back. Sometimes at first the book has the scent of the cat litter but over time that goes away and the smell of mildrew comes back.
I am not a scientist or a botanist or whoever is a specialist in molds and mildew. These are my guesses based on observation.
I note this applies also to book with a mildew or mold smell but no visable water, moisture, or mildew on the pages or covers.
From what I understand the mildew or mold or whatever it is can spread from one book to another thus it is not worth keeping one or more mildewed books on your bookshelf as they may ruin the non-infected books.