Within Teamwork Desk, you can delete a custom field to remove it from your site entirely.
Click your profile icon in the top right of your site and select Settings from the dropdown menu.
In the Settings area, go to the General section and choose the Custom Fields tab from the left sidebar.
The Custom Fields section will display a list of the existing custom fields on your site, both active and inactive.
Hover over the field you want to delete, and click the edit pencil to the right of the field.
Scroll to the bottom of the edit view, where you will see an option to Delete custom field.
You will be presented with a confirmation modal. Click Delete to confirm and remove the custom field.
For more information, see: Enabling or Disabling Custom Fields