Though Wolfram Programming Cloud (WPC) anonymous objects can not currently be deleted on the WPC website, it should be possible to delete them from desktop Mathematica. On the desktop get a list of anonymous objects:
Still on the desktop, copy and paste the CloudObject that you want to delete:
Note that you must paste in the whole CloudObject with its live link. Mouse over it to be sure that it's the real active thing.
Check back on the WPC website to verify that the file is gone!