If you’ve been so ham-fisted that you’ve not only cracked the surface epoxy/gel coat layer but crushed it to the point that actual tows of carbon are wandering free on the surface then I think you know the answer already.
Even if it’s not quite as bad as that, but the surface is cracked then the chances of water being absorbed between the plies and aiding delamination is high, so it’s still bin fodder.
The fact that it’s aluminium cored is to give you some residual strength if the carbon ‘rod’ fails (the aluminium tube will bend without the post just shearing off) – it won’t have enough strength in and of itself to compensate being damaged to the extent you describe and carry on working safely.