Ribbon cable reconect to IDC
"IDC" -> "Insulation displacement connector".

That's not an IDC connector, it's a flat flex cable (FFC). And yes, you should be able to reconnect it. There are typically small tabs on the mating connector that you can pull back, then you insert the cable, and then push the tabs back in to lock the cable into the connector. As long as you do not damage the tabs, these connectors can be connected/disconnected many times.