Select the offending files, press shift+delete, check the dialogue, press enter to commit.
That's how it works on Windows at least. If you just hit the delete key, you would get the attached prompt, and would need to select the 'nuke' option. Shift+delete shows the same prompt, with the 'nuke' option preselected.
If there's anything wildly different on a Mac, someone will correct this, I'm sure