Earny needs access to your email in order to find price drops on your purchases. He only receives a copy of the emailed receipt from retailers and communication regarding your price adjustment request.
Earny does not delete/manage your inbox. These permissions are setup by the major Email providers (Gmail, Microsoft, etc.). Earny does not have an option to amend these permissions.
However, you can always create an alternative email account such as YourNameShopping@gmail.com, and send your receipts there. Register to Earny with the new email and rest assured we will only receive your receipts.