I have heard of people having luck by using a business card and tearing off a piece and stuffing it in the spot where the plastic piece should go. I doubt it will work as well, but as long as it pushes the contacts of the ribbon cable up against the contacts of the connector, it should work. You could then tape it on with a piece electrical tape to help it stay that way.
It shouldn't have any effect on the LCD, as it is some what like unplugging a monitor cable, or not having it in all the way. I am not an expert, but I have broken many thing relating to a computer and I have never hurt a monitor with a ribbon cable.