Answer:
going through the screen.
Explanation:
In the office business people usually have people that screen various activities that need their attention. The screen categorises activities into important, not important, urgent, and not urgent.
The screens have great influence on what gets done in the office.
In this case Veronica is trying to convince the screen (prospect's subordinate) of the benefits of meeting with her.
She is trying to go through the screen to secure a meeting with the prospect.