This article walks through getting your Gmail account correctly configured while PeakMetrics' verification application awaits final approval from Google.
To start, select Sign in with Gmail, to begin connecting your Gmail account to PeakMetrics.
Choose the account that you would like to connect. Due to PeakMetrics' current pending application, a security notice will come up. Select "Advanced" and then "Go to peakm.com" to proceed with verification.
Google will then prompt you to allow PeakMetrics to read, compose, and send emails on your behalf. This is what allows PeakMetrics to create the outreach emails and actually send them from your domain (much in the same way that MacMail or Outlook works).