Okay, so just to be clear on the recent events. 
Damian fought Hyun. 
Damian won. 
Because of his weapon it is highly likely that she had poison. 
So he called Zenoram, really Zero, down.
Had him search for and remove any poison as he would be able to. 
Am I clear on this?

Just to be clear there is one of two ways removing the poison would be done. 
1) He would locate it, make a small incision, and suck it out. 
or
2) He would make a small incision, send in some of his own poison, collect any other poison and draw it out. 

Obviously, the second choice would be more painful. But both would be a lot quicker and easier to recover from than using an anti poison or drawing it out medically as not even the slightest trace would be left behind by the dragon slayer. 

Sorry... I have thought of a scenario in which Zero would draw poison from someone and these two were my favorite and seemed fairly plausible, as he cannot simply control poison that is not his own.