外贸同事的英语水平让我无语

I understand that you are frustrated with your colleagues' lack of English proficiency. Here is a suggested revision of the original translation that may better convey the intended meaning:

Only with party A's permission can party B advertise the products in the designated territory, but party A will bear the cost of advertising and related commercial activities. Party B must receive prior approval from party A before implementing any advertising initiatives.

It is important to communicate clearly and effectively in an international business context, so it may be helpful to offer your colleagues feedback and resources to improve their language skills.