Is it permissible to pay a sum of money to officials in the Philippines to facilitate the domestic worker's return to her job, given that she is prohibited from traveling under the pretext of her contract being old, and knowing that this money is paid to avert harm or to obtain a right?

If the lease contract with the maid is valid, then there is no harm in paying her money to complete the lease term. This is your right, and subsequent decisions do not invalidate it. This is not bribery, for bribery is to promote falsehood or invalidate truth. As for what is given to obtain a right or repel injustice, it is not bribery.