After logging into your websites administration area through your website.

1. Open edit window that the image is contained in
2. Right Click (Control Click Mac) on the image and select image properties
3. On the left side of the image properties window you will see "Border" Insert a 0 here
4. Click Ok
5. Click Update

Default in some browsers for a linked image is with a border, which is why if not specified some browser will show the linked image with a border and some show the same linked image without.