For one of the WordPress plugins, that Morning Train is developing, we had to remove the users opportunity to close the modal box.
Some research, for a simple solution, lead to this post: http://stackoverflow.com/questions/2452974/how-to-make-it-as-non-closable-thickbox-when-it-is-clicked-outside
The solution is simple. Just add
modal=true to the link:
<a href="#TB_inline?width=600&height=550&inlineId=my-content-id&modal=true" class="thickbox">View my inline content!</a>