I just redid both chainplates on our Bene... not the original fittings but a similar system.
..... My guess is a little gentle prying will allow me to lift it and expose the holes with the rods.
The 'cover' is held from below by two (almost hidden) screws in the overhead either side of the tie rod.
I did one side at a time, secured the mast with halyards, backed off the shrouds, disconnected and removed them from the deck fitting (you have original Beneteau setup so may have to totally unscrew the turnbuckle body from the bottom stud). There are two screws under the deck either side of the tie rod that hold the deck fitting in place.. The tie rod threads out up through that fitting, so maybe you don't need to remove that. Ours leaked around the 'ball' end of the tierod where some ancient Butyl had dried and cracked. We used Sikaflex to rebed the deck fittings and reseal the tie rod end. Fresh (quality) Butyl might do too..
You do have to thread the tie rod back into place so that may disturb the sealant somewhat; so I added sealant over the tie rod top between the shrouds after the tie rod was retightened.
Mark your turnbuckle settings AND tie rod thread position with masking tape first soas to get yourself back to the original settings.
Once one side was complete, we secured the other with halyards and repeated. Not a bad job, completed in about half a day.
If you are primarily leaking around the tie rod fitting the it may not be necessary to remove the deck fitting, but if you're going to all that trouble you may as well rebed that as well.
You can see the difference between fittings below but the basic physical arrangement is very similar.