Easy enough: You don’t. (Or, well, you can, but it’s not what you think.)
The [Edit] link after the title of each of your items only appears to you, and only because you’re logged in—your customers won’t see it.
It’s actually pretty useful —it gives you another way to access and edit items (see here for more), so if, say, you need to change the size of all five colors of your hand-crocheted washcloths, you can go to that category, click on the [Edit] link after the title of each washcloth, and edit it from the item page instead of having to go in through your admin console.
So no worries—you’re the only one who can see it. It’s all good.
