TLS terminates at Cloudflare, not at your origin. When a record is proxied (the orange cloud), CF holds the certificate the browser validates against and opens a separate connection to your server, so it sees plaintext on both sides and can rewrite the HTML on the way out. Same mechanism that makes the WAF and caching work, so it isn't specific to the analytics feature.

Worth checking which of your records are actually proxied. DNS-only ones (grey cloud) pass straight through and can't be touched.