Midori is a teenage girl. Which means she menstruates. How does she do this while being part of Seiji's arm?
She doesn't? She doesn't need to defecate either.
One assumes that, since her real body exists and needs care, it also goes through normal bodily functions such as menses. Her 'arm' body doesn't.
It seems to be only her torso on his hand, negating the problem entirely. That or since their circulatory systems are linked, it is taken away normally.
I don't think menstrual blood is normal, that's probably why it's not usually re-circulated.
Her real body probably does it for her, or the creator simply forgot about it. You can choose whichever.