We integrate with Gmail, Office 365 Business and Microsoft Exchange.
Due to the tight integration with your email provider, what happens in one is replicated in your account.
If you clear an email in Triage, it will archive the email in your inbox
If you archive the email in your inbox, it will clear it in Triage
If you move an email back to your inbox, it will appear in Triage
If you read the email in Triage, it will be marked as read in your inbox.
And vice versa
You cannot, however, delete an email from your account.