Documentation

Changing Domains

Since version 1.2, Offload S3 rewrites any S3 URLs to the local non-S3 version of media added within the main content of a post, page, or any other post type on save.

Offload S3 then filters the content on-the-fly for display and local URLs are rewritten to S3 URLs for the browser. This is important because if you change your domain, Offload S3 will no longer recognize those URLs as local URLs which it can rewrite because the domains will not match.

The solution is to run a search and replace on your database, specifically on the post_content and post_excerpt columns of the posts table.
Search: //old-domain.tld
Replace: //new-domain.tld

There are many tools available to do this, including WP Migrate DB Pro

Search and replace with Migrate DB Pro