To remove the border, follow these steps:

1. Go to your wordpress Admin CP.
2. Click on Presentation and the select the theme for which you want to add image border.
3. Click on “Theme Editor”
4. Open “Stylesheet” or “style.css” whatever from the right hand list.
5. Now you must be able see the CSS codes.

Now copy and paste this code in a new line after any “ } “ close tag.

img.wp-smiley{ border:none;}

This will remove the ugly borders around those smilies keeping image borders intact.

Before:                         Now: