Which AWS service should the company use to meet this requirement?

Explanations:

Amazon Elastic File System (EFS) is a scalable file storage service for use with AWS Cloud services and on-premises resources. However, it is not specifically designed for tape library integration or for extending backup storage capacity.

Amazon Elastic Block Store (EBS) provides block storage volumes for use with Amazon EC2 instances. While EBS can be used for storing data, it is not suited for extending tape library capacity and lacks the necessary integration for backup purposes.

Amazon S3 (Simple Storage Service) is an object storage service that provides scalable storage for data backups. While S3 is an excellent solution for data storage, it does not directly integrate with physical tape libraries without additional services or configurations.

AWS Storage Gateway is designed to connect on-premises environments with cloud storage. It provides a way to extend on-premises tape libraries to AWS by enabling a hybrid cloud storage solution, making it the ideal choice for integrating with the tape library for additional backup capacity.