I'm trying to delete a file, but I get a message from Trash saying:
"The operation can’t be completed because backup items can’t be modified."
What does that mean and how can I delete it?
According to this thread at Apple, this is a bug. This means it will hopefully be fixed in a coming update to OS X.
In the meantime, you have to relaunch the Finder, which you can do either through force quit (⎇⌘⎋, or through the menu), or by less violent means by quitting it normally, which you must first activate through the following command issued in the Terminal:
The root of the cause
Time Machine backups are protected at kernel level -- on a verbose boot it's possible to spot in the first screenful of text a
Deleting in Time Machine
The officially sanctioned method for deleting items from a specific backup or all of them is to locate the item in the "in space" Time Machine view and selecting the appropriate delete option from the contextual menu or the Action button in the toolbar.
The ability to move backups to the Trash added in Lion is not only comparatively more buggy, but designed to operate on entire snapshots, i.e. the folders named with the time the backup was created which in turn contain a directory for each included volume.
Deleting from commandline (more flexible, more control)
In Lion you run:
In Mountain Lion