The glass is held flush by that bottom bracket. I'm thinking he stuck that in there to keep it more flush to the machine perhaps?
You may just have to remove that top glass and bend in that bracket a little. Or just use a brown Sharpie pen and color the exposed part of the dowel brown and leave it alone.
The other possibility is the bottom part of the glass could be chipped or damaged and the wood is there to cover over it.
To remove the glass you have to push it upward, then pull the bottom out, but be CAREFUL!
Here's two photos from my machine. Hope this helps.