I was going through the google drive picker api docs, I didn't find the proper solution to handle the delete files/folder(s) through the picker.
I just wanted to confirm that google picker support the delete functionality or not?
Drive Picker API
It is a limitation or feature missing itself from the Drive picker. It is generally designed or used to view data that is available to be accessed, deleted files would not be considered as available data to be used, it would require the manual restoration process.
As an alternative or request for either documentation or feature, you should be able to open an Issue tracker:
References: