Paper lice feed on "spores" of a certain fungus so if books have spores, the lice eat the paper too.
The fungus grows in damp areas.
Paper can be treated with insecticide to avoid this damage.
But many rare books cannot stand insecticide treatment.

Conclusion:
Dehumidifying will allow rare books to be stored without risking damage from paper lice.

Note that the conclusion is talking about damage from paper lice only, not any other kind of damage. So the assumption has to deal with damage from paper lice only.

A. Paper lice can be prevented from entering an area that is being dehumidified.

Irrelevant. We aim to get rid of the spores on the paper that they feed on. If we are able to do that, it doesn't matter whether lice are present or not. They will not eat the paper of the books.

B. Treating rare books with insecticide will cause more significant damage than that caused by paper lice.

Irrelevant. We are only concerned about whether dehumidifying will avoid damage by paper lice or not.

C. After the fungus has been eliminated, fungal spores do not remain in any significant quantity.

Correct. We are given that the fungus grows in humid environments. Dehumidifying will take care of the fungus but will it take care of the spores of the fungus too? We don't know. We are assuming that it will and that is why we are concluding that lice will not eat paper anymore.

D. It is possible to store rare books in a dry environment without causing the pages to become brittle and crack.

Irrelevant. We are only concerned about whether dehumidifying will avoid damage by paper lice or not. What other damage dehumidifying can cause doesn't matter. We are not concluding that books will be safe if we dehumidify. We are only concluding that books will be safe from paper lice.

E. No other insects, aside from paper lice, typically feed on the paper used to create books.

Again, irrelevant. Any other kind of damage has no relevance to our argument.

Answer (C)