Sadly it is not possible to download the .fit file using iOS, I’m sorry.
Also, I went through the documentation for the Cyclemeter applicaiton and it appears that it does not support automatic importing of Strava like most third-party apps do; I apoligize for the confusion there. Unfortunately, all workouts need to be imported manually using GPX, TCX, or FIT files.
What this means, is that you will need to use a Mac or Windows device to download the .fit file and manually upload to Cyclemeter to keep things in sync. There doesn’t appear to be a way to do this completely on a mobile device.