Edit: I found a solution--see my answer below.
The answers I've read are old and no longer work (possibly because Microsoft makes substantial changes to the UI on a regular basis).
I tried File -> Options and settings -> Data source settings, which makes this box pop up:
Data source settings popup window
There's no option here to delete data sources. Right clicking just gives the same options as below: Change Source, Edit Permissions, and Clear Permissions. "Clear Permissions" does not remove a file.
I need to remove two of these because they were added in error. One of the files no longer exists, so the Refresh function no longer works. Any ideas would be much appreciated. Thanks!