When I created my iOS project in Xcode 5 I clicked the option to add testing to the project. Is it possible to remove all that testing stuff, just as though I hadn't clicked the option to begin with?
I suggest to make test in your project.
But in any case, you might to leave there the target.
Otherwise, if you want delete at any cost, you have just to click on your project settings and click on this icon:
You will see your targets and you will can delete the test target. At this point you might want delete the test classes too: on the folder hierarchy, select these and just press backspace, confirming the deletion.