@nr2012 I am facing the same problem. I use WP as a headless CMS for our company blog. Would you be able to describe the steps involved for adding the filter?
add_filter('rest_url', function($url) {
// removing /wp at the end of site_url
$pattern = '/(\S+)(\/wp\/?)$/';
$siteURL = preg_replace($pattern, '${1}', site_url());
$url = str_replace(home_url(), $siteURL, $url);
return $url;
});