Greetings PJ888,
I am with Adam on this one, I bet the plastic parts are keep the expansion panel in place and secure for moving or shipment. Is the property a rental? Can you contact a landlord or maintenance team that may have experience with the table? If it is a rental property the panel may have been secured so that it is not easily removed.
One other option: most furniture will have the manufacturers name imprinted somewhere on the piece, you can call them and see if the plastic braces are part of a shipping method.
Once again Adam is correct, pictures would be helpful!
We will wait for your response to better assist you,
Good luck! Maureen