Can you post the picture showing the breakage? I am not honestly not getting it from the picture unless it is just sample picture.
You will probably not believe me but you might even be able to duct tape it back because the oil there will not be under pressure. Seriously look in to re-threading/epoxying it shut. On many Hondas, that hole is used for some post purchase aka TSB use i.e. even the Honda dealers can NOT use that place to fill in the transmission as oil jet passage is put there. I do not see any downside to shutting down the whole area. Your aim is to make sure that the repair is leak-proof to transmission oil. Use appropriate chemical or mechanical means to achieve it. Replacing the case means replacing the transmission itself. You are talking about multiple thousand dollars. Unless you have money tree growing in the backyard, don't go there.
And yes, try to differentiate between a screw and a bolt

Seriously, even though I can't give you the exact definition of each, I know it when I see it.