I'm confused a bit (I don't think I've ever NOT been confused... but that's another story LOL). But I think I know what you mean.
Here's a way to change or "get rid" of icons that you've messed up. Let's try this:
Locate the file that has the goofy icon.
Click ONCE on the file. You're only clicking ONCE on it to bring attention to it. Don't double click it, because you are not wanting to open it up or run it.
Just click it ONCE (you'll notice how the file's name just turned dark).
Now, go up to the word, "File," in the top left corner of your monitor, and down to "Get Info."
In the top left hand corner of the new little window that just popped up, you will see the small icon that you are disliking.
Click ONCE on that small little icon (that will darken it).
Now, go up to the word "Edit" near the top left of your monitor.
Now, click on the word "Cut."
That will get rid of an icon you accidentally put onto something.
If the word "Cut" is greyed out, or, nothing happens when you click on "Cut," then that means something else is going on.
Hope that helps.