How do I avoid checking for updates for a specific module?
You need to implement hook_update_projects_alter(). 


  Alter the list of projects before fetching data and comparing versions.
  
  Most modules will never need to implement this hook. It is for advanced interaction with the update status module: mere mortals need not apply. The primary use-case for this hook is to add projects to the list, for example, to provide update status data on disabled modules and themes. A contributed module might want to hide projects from the list, for example, if there is a site-specific module that doesn't have any official releases, that module could remove itself from this list to avoid "No available releases found" warnings on the available updates report. In rare cases, a module might want to alter
  the data associated with a project already in the list.