[Fr. Frank]

I'm going to presume that the majority of these screw are near the bottom of the transom. I'm also going to presume that you have not examined the wood around where the motor mounting bolts go through the transom. If you're going to replace a part of the transom core, for 30% more effort you can replace the entire core, which I recommend. That way, you know you've got a good transom.

Using a 4" angle grinder equipped with a saw blade, you can cut the old fiberglass away from the wood. It's a nasty, dirty job. You cut through the fiberglas into the wood, in an outline pattern about 1/2" in from the edge all the way around the edges of the transom. If you want to install a bracket, or raise the transom, this is the time to do it.

Using a hand chisel, or an air chisel, peel the fiberglass away from the wood core of the transom in a single large sheet. Save this very carefully, you'll need it later.

Now grind, chisel, sand, vacuum, and cuss the old core out.
You can use the transom skin as a template, to make a new core out of your preferred material.

How do you put it all back together? Not a clue
Seriously, I've replaced one transom by myself in my life, 22 years ago. I made a mess of putting it back together. I've helped two friends remove their old transom cores, but I did not help them put them back together. Every time I try to use fiberglass, it looks like I turned a 5 yr. old loose with Play Doh that got real hard. So I don't do that stuff.

I will be redoing the transom on my boat in a couple of years to close it in and mount a flotation bracket. I will take it apart, but I will not put it back together. I'll buy the beer for all the friends for whom I've rigged, or towed, their boats, or rewired them or something. A couple of them are real good with fiberglass and gelcoat, thanks be to God.

Good luck.