Hello Kylie,
could you please try to repeat a delete operation an take a look to system log (i.e through /Applications/Utilities/Console), if there’s a more detailed information? The path you have mentioned looks like you backup your computer (i.e. using parallels) to your external drive. In such a case I’m not sure, if the partition is mounted as writable and what would be reaction of a backup tool, if you would delete these files manually. Otherwise, if there is not a bug in avast! code and if your user account is among computer administrators, I would expect that you should be asked to enter a password during a delete operation and then the file should be deleted with a superuser permissions.

Best Regards,
Martin