Where do views/panels get their source html code
It will depend on the contents of the panel or view display as to the actual content to be displayed.  For example a panel/view might contain a node, in which case a specific display mode would be used dependant on the output settings.  Using your example whichever module provides the Format: Bootstrap Thumbnails is likely to be the candidate which can either be further overridden with a different template, or with an appropriate hook_theme.