The contacts are removed from the back of the connector, but they are released from the front. The next TWO PICTURES show the miniature screw driver inserted in the connector contact hole. A very LIGHT PRESSURE is needed to remove the pin. I have found that a very slight twist is the easiest way to bend the tab down.Twist one way then try pulling on the wire, if it doesn't come out twist the screw driver the other way and pull the wire again. Remember use LIGHT PRESSURE and a very minimal twist. It may take several tries to get the contact to release.
NOTE: The connectors shown are damaged. I used these for ease of illustration of the contact removal process.