Check SMTP connection in health check

I have created a web service which can also send emails (using Gmail SMTP). This is deployed using Kubernetes and a health check is run every 30 seconds.

Since a team member changed the login credentials we use for sending emails, a check for the SMTP connection has been added as part of the health check. Now the health check tends to fail with the following error:

Invalid login: 454 4.7.0 Too many login attempts, please try again later. - gsmtp 

Should verifying the SMTP connection be part a health check? Or would it be better to just skip this check? Most of the system can still function properly without using SMTP.