Facebook's comment system makes it easy to share what you think when your friends post status updates and Wall posts. The comments on comments feature lets you specifically respond to other comments in the form of a mini thread. Unfortunately, it is not uncommon to post a comment without thinking to much about it only to realise a few seconds later that maybe you shouldn't have. You can easily delete a comment that you posted under someone else's comment on Facebook.
Navigate to Facebook.com and log in to your account.
Locate the comment you posted under someone else's comment that you want to remove. You can find a list of your activity on your profile if you can't find it.
Hold your mouse over the comment and then click the "X" when it appears. Click "Remove" when prompted by Facebook to remove your comment.