This is a bit unusual then because Malwarebytes ADWCleaner is a portable tool rather than installed. Do you still have ADWCleaner on your PC somewhere? If so I'd delete that and then try deleting it from the Virus Chest.
But that lead me to think: did you use ADWCleaner from a flash drive or other attached storage device. Is that same device actually still connected? If not then that is likely the problem preventing you from deleting it. If you or the PC have changed the ID of that device since ie. assigned a new drive letter you'd have the same problem.
If not this then, annoyingly, at the first scan ADWCleaner does create a folder on the root of the primary drive, typically C:\AdwCleaner. This can be deleted as it is regenerated each time so if the above two ideas don't work I'm wondering if doing that may solve the problem.
Have you tried restoring the files to their original location, one at a time and deleting them there in the normal way.
Final suggestion is to start the PC in Safe Mode and try deleting them from the Virus Chest again.
The question all this raises is why did AVAST send this, if that is what it genuinely is, well known adware remover to the virus chest? I would have thought the ADWCleaner would have been more likely to flag AVAST as problem rather than the other way around.
Only joking