ETA: I would prefer that you not do this for anything in my journal that is filtered, locked, or otherwise not public. There is a way to disable this for your account and remove the buttons (though, sadly, not for everybody else).
ETA: This is no longer true. You can now remove anyone's ability to repost from your journal using these steps, which I promise are simpler than the ones we used below. Kay? Kay!
This was mentioned in the news post on this issue but I thought a step-by-step guide would be helpful for people.
1) First, you must be using Firefox as your web browser. If you aren't already, you can download it here. It will give you the option to copy over your bookmarks, preferences, et cetera from whatever browser you were using previously.
2) Second, you install Greasemonkey. Greasemonkey is a Firefox add-on (and if you're new to this concept, the other add-on you should install is AdBlockPlus, which makes all the annoying ads vanish). Go to this link, click the green button that says "Add to Firefox." A dialogue box will pop up, which will make you wait a few seconds before you click "Install" in case you were in error. To make the changes final, you must restart Firefox.
3) Third, you install the script created to make those buttons go away. Go to this page and click the green button marked "Install" in the upper left. Again, a dialogue box will confirm this.
And hey presto! The buttons are gone, along with the fear you may click them without meaning to. Thanks, fearless script creator daluci!