As of this writing, it is not possible to delete a meta value using the WordPress REST API. Post meta updates must be communicated while inserting and updating post objects, and the only way to “remove” meta fields is to write blank values over their current values.
I wrote a free and open-source plugin to provide granular control over post and term meta fields. It lives on Github. The plugin is called Manipulate Meta with the WP API, and it extends the REST API to allow one request to retrieve, update, or delete a meta field independently from a post or term object.
Adds routes to the REST API to read, write, and delete post and term meta values separately from posts.
The instructions are located in the repo’s README.md.