First, gently push the tip of a spudger under the metal buckle of the display cable connector to unclip it, then swing it over the socket.

Next, hold the buckle and cable together and gently pull the connector straight out of its socket.

To reconnect:

Grip the cable and buckle together and insert the connector fully into its socket.

Aligning the connector can be tricky. Reposition it as necessary and don't try to force it into the socket, or you may damage both the connector and its socket.

Flip the buckle over the socket and use a spudger to press the buckle down until it clicks into place.