I'm not sure what else to tell you, the highest voted comment on YouTube explained it very well.
Teddy has a fear of water based on the incident that happened in the past that he is trying to suppress. Water and fire are the important themes throughout the movie
- Beach Cave
As the YouTube user correctly mentions, the audience is seeing the absence of water through the eyes of Teddy. In order to maintain control of what he believes to be true, he must cancel out any occurrence of water. Otherwise, it will resurface what really happened to the children.
There are three angles
- One facing across the table showing the marshal, the woman and Teddy
- One facing the woman, notice we see her right side, based on the seating setup, this is exactly where Teddy is sitting. The water comes from the marshal and she leans to the left to get it.
- The side from the woman when she finishes
The circle (water print) left could honestly just be seen as residual from the previous trials of the scene. If you notice the cut from when she drops back the camera angle across the table the ordering of the papers are not the same. Also, there is no pen in sight before the cut.