Administrator permissions are required to remove Email Campaign tracking data from the Email Campaigns and the Contacts/Leads.

Each data record in Salesforce is a minimum of 2k. This can mean that previously synchronized complete/old email campaigns can occupy data space unnecessary in Salesforce. To remove Email Campaigns statistics that are no longer required, first follow the FAQ for restricting Email Behavior Tracking Data.

Navigate to Email Campaign tab
Locate the Email Campaign where the data is to be removed or reduced.
Delete the Email Campaign (this will remove it from the list and all the associated data in the Leads/Contacts
At the next scheduled Email Campaign Synchronization (or use Synchronize Emails Campaigns button) the Email Campaign will re-appear in the list and will only import the behavioral data as selected in the Email Campaigns Data Options. The contacts/leads will also be populated with the selected data.

The data will need to be removed from the Salesforce Recycle Bin before the Salesforce storage is reduced.