Well, it was successful! I was able to unscrew the "valve covers" and take the little yellow/white disks out. Not having the wrench, I used the corners of some square jawed pliers to jab in the holes on the covers and unscrew them. Not ideal, but it did work. The disks are indeed quite small! Maybe 2mm. There was some gunk inside the valves, on the disks, and in the vent holes. So I cleaned everything and reassembled the valves, after the reline/add palate operation.
The doctor reports that the denture stays in fine. So that's a relief! I was concerned that the little disks would be too hard and wouldn't seal. But apparently not. With the palate, the doctor could just stop the holes up if the retention proves unsatisfactory. I get the impression that the patient wants to keep the valves.
Thanks, everyone, for the help!