A light wipe of the cable's exposed black conductive surfaces (i use a Kleenex tissue. Then the cable simply slips out of the connector. There is a delicate plastic 'bail' that needs to be pushed about 1 millimeter away from the connector body (along the cable). See the flat cable to the display? It is held to the circuit card by what is called a 'zero insertion force' (ZIF) connector.
If it's the display module itself, then the approach is to unscrew the 4 screws holding the case together, then the internal screws that hold the circuit card against the front face. Inspect closely and clean carefully (don't dislodge the springy contact wires from their individual slots). (it could also simply be dust/dirt contamination of the sockets themselves (both HBX end and scope end). If you have a 'telephone handset' cord (the one that went between the lump on the wall/desk to the thing you held to your ear), you could use that as a HBX cable and see if the symptoms change. If the HBX cable is 'going bad' on the wire going to the handbox, the intermittent issues can inject (or corrupt) the bits being sent towards the screen. If the telescope is otherwise operating correctly, then the problem is usually limited to the wiring going to the handbox, or the display module (and its cable) itself.