After installing “Visual Studio Extensions for Windows Library for JavaScript” update, it still appears as an available update

Try this workaround:

http://connect.microsoft.com/VisualStudio/feedback/details/847258/vs2013-keep-saying-windows-library-for-javascript-needs-updating-1-0-9651-40228

1. Get “msiinv” from here: http://blogs.msdn.com/b/astebner/archive/2005/07/01/using-msiinv-to-gather-information-about-what-is-installed-on-a-computer.aspx
2. Run msiinv.exe -p > out.txt
3. Open “out.txt” and find “Visual Studio Extensions for Windows Library for JavaScript”. There should be two of them, one with version 1.x and second with version 2.1.
4. Lookup the product code for v1.x and uninstall it using msiexec /x. For me, the product code was {D5FEB7A1-5D0F-4CDC-8290-F52DFB53AF23}, so I ran
   msiexec /x {D5FEB7A1-5D0F-4CDC-8290-F52DFB53AF23}

If you need to reinstall the extension, you can get it here:
http://www.microsoft.com/en-us/download/details.aspx?id=40793