You can only Delete a Contact if there aren't any references to it anywhere in FastBound. That means that if there are any Items Acquired from, Disposed to, or if any changes have been made to the Contact, you cannot Delete it.
To Delete a Contact
From the Main Menu click 'Contacts'
Select the Contact from the Contacts List or Search for the Contact
In the Contact Information Panel Click the 'Delete' button
Verify you want to Delete the Contact
Click the 'Delete' button
Once a Contact has been Deleted it cannot be restored, it must be created again.
If you cannot delete your contact you can Archive it.