Remove all Wordpress HTTP headers (not in-source embeds)

Question

When we do CURL on our domain, there are things added to the header:

server: nginx
date: Sun, 27 May 2018 01:05:34 GMT
content-type: text/html; charset=UTF-8
vary: Accept-Encoding
link: <https://EXAMPLE.com/wp-json/>; rel="https://api.w.org/"
z_sk_cache: 0

It's that JSON thing we'd like to get rid of. Any way to do this? All google and StackExchange searches are about disabling "embeds" like emojis or json. But we don't use wp_head() in our theme at all, so none of those are an issue. It's these pesky HTTP headers that are added from somewhere inside WP and we'd like to get rid of them.

Welcome thoughts. Thanks.