Deleting a contact in CircleBack will NOT remove it from your device unless you have enabled address book sync. If sync is enabled, changes to contacts in CircleBack will be reflected within those same contacts on your device. If you wish to manage contacts within CircleBack without impacting the contact list on your device, make sure sync is disabled.
By default, sync is disabled. You can check your sync settings through the Settings menu within the app. More information regarding sync can be found here: https://circleback.zendesk.com/forums/22995333-Syncing