FileSystemResource does not appear to close the InputStream that it creates.
I believe it should call setClose(true) on the PartWriterCallback.
To verify the problem, see the attached quick start. Change the filename in HomePage.java to point to some valid image file on your system. After viewing the home page in a browser, check for files that the jetty process has open, eg:
If you load the home page a few more times, using Shift-reload to avoid simply loading from cache, you can see many file descriptors pointing to the image file are kept open: