Preview comment / parent-delete-edit newbie problem

Small usability problem:
When previewing a comment, the texts "parent" "delete" "edit" "reply" etc. are shown.

To a newbie (specifically, my mom), this is confusing, and clicking on "parent" for example will abandon the comment and try to perform an action on a comment that doesn't yet exist. It was unclear to her that the idea was to click on the "Post comment" button a bit further down the page.

I think it would help to somehow remove these links from the default comment (and node?) preview mode. Maybe they can stay, but they shouldn't be clickable at that point.