For those unfamiliar with this disorder, click here for more information.
The basic concept of treating this rare disorder is that there is a common wall that divides the esophagus from the diverticulum pouch. This common wall is endoscopically divided such that the pouch now becomes the new back wall of the esophagus. So when the patient swallows, food/liquids can no longer get "trapped" causing symptoms.
Still confused? Here are some picture illustrations...
When endoscopically exposed, the pouch is denoted by the arrow.
Here is the side view before and after common wall division:
After the procedure, any food/liquid substances that are swallowed can't be trapped in the pouch. Therefore, even though nothing is surgically removed, the patient's swallowing symptoms completely disappear.
Hopefully, this explanation helps clear up any confusion of what exactly happens!