This option is the most efficient because it uses a gateway VPC endpoint for Amazon S3, which provides reliable connectivity to Amazon S3 without requiring an internet gateway or a NAT device for the VPC1. A gateway VPC endpoint routes traffic from the VPC to Amazon S3 using a prefix list for the service and does not leave the AWS network2. This meets the requirement of not traversing the internet. Option A is less efficient because it uses a private hosted zone by using Amazon Route 53, which is a DNS service that allows you to create custom domain names for your resources within your VPC3. However, this does not provide connectivity to Amazon S3 without an internet gateway or a NAT device. Option C is less efficient because it uses a NAT gateway to access the S3 bucket, which is a highly available, managed Network Address Translation (NAT) service that enables instances in a private subnet to connect to the internet or other AWS services, but prevents the internet from initiating a connection with those instances4. However, this does not meet the requirement of not traversing the internet. Option D is less efficient because it uses an AWS Site-to-Site VPN connection between the VPC and the S3 bucket, which is a secure and encrypted network connection between your on-premises network and your VPC. However, this does not meet the requirement of not traversing the internet.