With what right?

Long Ju and Xie Li were not married. Xie Li was her possession if she were to put it nicely, or a slave that Long Ju took it as her own if she were to put it in a bad way. 

No matter what, the two of them did not share any legal relationship, which meant that even if Mo Qiang fought for it. She would not be able to get an alimony from Long Ju for Xie Li and his child, if that was the case, then she would have to get what she wanted indirectly. 

By making Long Ju sign this contract, Mo Qiang would be able to make sure that Long Ju would pay a certain amount as alimony to Xie Li. Since this woman believed that she could do anything that she wanted, Mo Qiang was going to take the responsibility of teaching Long Ju a lesson that every action had a positive or negative consequence. 

Depending on the action.