Bridge Plate
Sometimes called "bridge patch"
On the inside of the guitar top, just beneath the bridge, there is a "bridge plate," a layer of hardwood which protects the top from damage where the string balls pull up against the top:
Almost all flat top guitars, including many classical guitars, have bridge plates even if they don't have pin bridges.
The bridge plate serves an important function to ensure the stability of the bridge and top glue joint. The bridge plate increases the stiffness of the top in that area, and reduces the tendency of the bridge to "peel" off the top.