You could delete both Full-Time and Occasional Agents from your Freshdesk Account. To delete an agent, please navigate to Admin --> Team --> Agents. You would view the list of agents on your Account and the delete option corresponding to the Agents' name. You could click on the delete button, which would remove the contact from the Agents list.
When an agent is deleted, they would be converted to a Customer on your account. Their profile could be found under the Customers tab on your Freshdesk.