What can I do if the recipient doesn't remove the illegal links?
What happens if the host of the infringing content does not respond?
Most of the time, webhosters will answer your requests to remove content, having no interest in hosting pages whose content is illegal.
It is sometimes useful to renew content deletion request mailings: recipients will understand how you follow and update your DMCA requests in this way, prompting them to delete the relevant pages.
Some webmasters use CDNs (Cloudflare,...) and voluntarily hide information related to the original server. This sometimes for security reasons, but most of the time to avoid being spotted.
In this case, you will have to use the form provided by the CDN and fill it out manually to send your DMCA takedown notices directly with the CDN. The DMCA form for Cloudflare is here: https://www.cloudflare.com/abuse/form