That's not how the law works, though. You can't force medical operations etc on people, and you compel people just because your resources were used in medical operations on them. There is no such thing as "partial ownership of the own body".
Basically, just speaking about legalities and not de facto powers, all NERV could do would be to charge Mari for misuse of NERV resources. Unless, as said, slavery has been reintroduced in the meanwhile.
/E: I mean, if a person embezzles company money to get a cardiac pacemaker for a relative, and this embezzlement blows up, the company wouldn't be able to demand that cardiac pacemaker. The embezzler would simply have to return the embezzled money as much as he still can.