I do believe it is used as a stiffener and being wood it flexes without breaking. What else do you have on the other side to compensate for this wood if you were to remove it?
You would not want to pull it out and then try a hole shot only to watch your transom cave in towards you in the middle.
You might consider using the piece of wood as a pattern and cut yourself a piece of starboard = High-density polyethylene (HDPE) to match the size and shape of the wood is one suggestion.
The white HDPE is not UV resistant. Only the black starboard HDPE is UV resistant and used in boats. If you replaced the wood with starboard it might outlive you!
Make sure to use a good marine sealant on the entire face of the plastic to metal because if water is allowed to get down inside, galvinic corrosion can happen. So you will want to permanently seal out any water from getting in between. I would also chemically treat the aluminum with something like zinc chromate or the replacement for it. You can get a spray paint can of it at any auto parts store or home depot for about $5.00, and treat the surface of the aluminum with something designed to prevent corrosion. Then glue the new piece in place, put bolts back in and forget about it!
Check around for pricing on HDPE. It is expensive and cheap pieces can be found in side ALRO or various plastics companies who have cut pieces for sale. Otherwise they will want you buy a whole sheet of it. And don't try to paint it. Not much will stick to HDPE.
