You don't need to do anything in the head section yourself. JFBConnect has many options to either automatically set the image, or let you set it without mucking with your template.
To set the Like image for a specific page, you have a few options:
* Install an Open Graph plugin for the component that's rendering the page. So, if it's a Joomla Content page, install and enable the Open Graph - Content plugin. That will automatically set the first image in any article text as the Open Graph image for that page. There are also ways to have more control over the title, description, or image used by configure your Open Graph settings
* On the specific page that is being liked, add {SCOpenGraph image=http://site.com/image.jpg}, pointing to the image you want to use, and JFBConnect will force that to be the Open Graph image tag
* In the Open Graph -> Settings area, you can set a default image that will be used across your whole site. That's good for a logo or something that will be used if no other image is set (preventing a banner ad or something else from being selected by Facebook).
Once you set a better image, you can use Facebook's URL Debug Tool to refresh their cache of the details about that page:
developers.facebook.com/tools/debug
Once refreshed, the Like your client made should update with the new image in a few minutes to an hour or so. If not, then yeah, just un-like and re-like.
Hope that all makes sense, but if not, let us know,
Alex