If you are talking about the latch for the top screen flexible cable, here I put some examples about these type of connectors:
As you can see the black or brown latches are there to press the flexible cable contacts down to the connector contacts and avoid the flexible cable to unplug accidentally. All you need to do is lift the latch and then the flexible will be free to take it out.
In the case of the other black wires, you just need to lift the plated connectors.
I recommend you to roll up the flexible cable and use tape to avoid damage to it when taking it throught the hinge. Thats because if you damage the cable then you must but a complette new top screen because the flexible is soldered directly to the LCD screen.