The climate control wood trim is very easy to replace. Use a pry tool to get behind it at the top edge and gently pry it forward.
The trim piece is simply held in by four pegs that pop in to the climate control unit behind the trim, there are no screws.
The only precaution is to be sure that you are prying from behind the entire trim piece, and not prying between the wood and the metal backing. Otherwise you might pull the wood away from the backing, damaging both.