The trash, and dragging files out
Two ways a file leaves the window: into the trash, or into a folder you drag it onto.
Moving to the trash
Select what you no longer want and use Move to Trash from the menu, ⌫, or ⌘⌫ from the File menu.
The app asks first, and the question names how many items it is about. Once you are sure you do not want asking, switch Ask for confirmation before moving items to the trash off in Settings.
Either way the files go to the macOS trash and not away for good, so they can be put back until you empty it.
Dragging files out
Drag one or more selected thumbnails out of the window and drop them on a folder in the Finder, or on any other application that accepts files.
This moves the files, exactly as dragging them in the Finder would. Hold ⌥ down as you drop to copy them instead, leaving the originals where they were.
It is the fastest way to use a scan for what a scan is often for: finding the twelve pictures from one afternoon that are scattered across three folders, and putting them in one place.
The window will not offer to take a drop unless what you are dragging in contains a directory, so dragging files back onto AssetScout does nothing. Dragging out works with anything selected.
When a file will not move
macOS can refuse. The usual reasons are a locked file, a read-only disk, and a network volume with no trash of its own. The message names the files it happened to.