The wood in the 'space' would have been checkered as in this next picture. Your skeleton steel buttplate was removed and a rubber recoil pad was installed. The rubber is gone but the plastic or hard rubber base plate of the pad is still there. There is a remote chance that the checkering is still under that base plate but I doubt it.
As long as the condition of the barrels are safe to shoot and they are not 'off face' of the frame I would think it is safe to shoot.
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