I should also mention recruiters. They get one-off payments from Chinese employers for introducing FTs. The main difference between recruiters and agents is that agents pay the FTs monthly after deducting commission from the monies paid to them by the workplaces where the FTs were sent. In contrast, the workplaces where the recruiters introduced the FTs pay the FTs direct.

The problem I have is that you are choosing to re-name , because most of these 'agents' in fact call themselves schools, don't they?

According to this forum China is covered in Training Centres who don't actually train any-body in the accepted sense that such a term is customarily used for ,like, 'Teachers' Training College'