If you wish to limit your Outbox and Activity Feed to prospect mailings only, this can be done from the org settings menu from an admin account in Outreach. The setting is located in Org Settings, below the "Block creation of prospects..." setting. The setting is visible/controllable by org admins only. In order for this to work effectively, orgs will need to be sure to add their own domains to the "Block prospect creation" setting and ensure that no prospects currently exist for internal employees.
With this filter on, non-prospect mailings are not accessible to users in that org.
If you wish to see all mailings in the Outbox/Activity Feed (prospect or not), please uncheck this checkbox.
One additional caveat to this setting is that if a user emails someone from Outreach who is not a prospect (i.e. with a one-off compose), that email will now no longer show in the Outbox. If this is a common scenario for one of your users, you can disable the setting.