To delete a contact from Talkdesk, you will need to start by locating it in your "Contacts" section.
You can search for contacts (and sort contact lists) by the contact’s first or last name (“Name”), the contact’s email (“Email”), the company the contact works for (“Company”) or their phone number (“Number”).
Open the contact by clicking either the name or phone number. Then, click the Settings button  and select Delete Contact :
Note: Deleting a contact will only delete the contact’s profile information. All calls and data related to that contact will still remain accessible on your Calls list and the contact's history. To delete Contact history/activity, please send a request to firstname.lastname@example.org prior to the deletion of the Contact.