I put a coat or two of varnish on those pieces every year, in place. When sanding I protect the acrylic with blue painter's tape. Taking them off is a major project to avoid if possible (see below).
I'd use a heat gun if necessary, gingerly of course, with some aluminum foil to protect the plastic.
From a
blog entry:
The sliding hatch has two pieces of teak to get off: the lower piece, which sustains the radius, and the upper handle we pull to open it. Both wood sections are fastened by #12 stainless wood screws. They're offset, so one set of screws is angled but the other isn't. Furthermore, the wood is sealed to the plastic with black Dow 795 or something similar.
Since the teak is critical to the appearance of the yacht, it needs to come off without damage. But the plugs are very deep and resist extraction, and their holes must not be buggered. The best idea is to drill them out with a 3/8th Forstner bit. The buried screw heads are fouled with varnish, and I spent too long cleaning them and then slowly working the screws out. Better to just sever them with a Dremel saw and be done with it, as I did for the final two.
The Dremel is also by far the best way to free the wood from its sealant bond. A chisel damages the teak, and a putty knife--forgetaboutit. Care removing the wood means not having to make new teak pieces later.
The view below is the underside of the companionway hatch. Screws enter it direct from the plastic surface. Screws from the wood on the other side penetrate through the wood, the plastic, and into the underside mating piece---at an angle. In Craig's shop I set both pieces of wood in place so he could drill the angles through the acrylic guided by the existing holes.