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 blog posts 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 blog posts (see here for more), so if, say, you’re reading through recent blog posts and find a typo, you can just click on the [Edit] link to get to the post 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.
