Just discovered in Build 4.0.57.30 (2019-04-05) there is a bug when it comes to Delete Contact Information. So if you have a CLIENT and you want to be able to Add Contact Information to the client and then Delete Contact Information from the client, the Delete Contact Information right in Client Information > Client Details > Contact Information right is what it should be and it governs the appearance of a Delete icon button.

However, you get an error after you click delete if you don’t also have the right Delete Contact Records which is in People > Contacts which is a completely different part of the software.