Symptom: certificate verification failed for smtp.sendgrid.net, untrusted issuer.
1. The connection is still encrypted. The failure is only that your server cannot confirm the certificate chain.
2. Install the CA bundle on the sending server. The doc points at the GoDaddy CA bundle (SendGrid's cert chain) as the missing piece.
3. Tell your mail server where the bundle is (for Postfix, the smtp_tls_CAfile setting) and restart it.
4. If the server talks to many providers, add the cert to the existing system CA bundle instead of replacing it.
5. Do not fix this by disabling verification. That trades a config task for a real MITM hole.
After the fix, a test send over 587 with TLS should complete the handshake without warnings.