You can't delete a file using OS X Simple Finder.
Yes, we all know that the Finder is flawed, that Apple broke their beautiful Classic OS file indirection system with OS X, that Apple's metadata management (file type, creator, etc) was screwed up in OS X compared to classic, and that OS X's smb network services are feeble -- but these are all minor flaws compared to Simple Finder. At first glance this looks like a great way to introduce a non-expert users to OS X, but the pretty face is deceiving. Simple Finder in Mac Classic (OS 8+) was a great piece of work, in OS X it's proof positive that Apple can be as incompetent as Microsoft.
Don't do what I did. Don't spend hours trying to make Simple Finder work as a user environment.