I was in same case before.
This all depends what commitment you and your maid made. Mine was 50/50, but she said no money. So, I'd paid all then deducted from her 1st salary.
Unfortunately, she is the worst among all my ex-maids even she was introduced by my relative. She is my 3rd maid, after her, the 4th, the current one is good and work for me nearly 8 years.
I spent much more money on this worst maid even pay 1/2 agency fee.
As I remember, self-hire no special offer from agency since they actually ask high commission from the maid if the job is introduced by them.
May be you ask the agency to disclose how much the maid should pay if the job is introduced by them. Then, ask she bear her own and you just to pay the same as you hire maid thru the agency.