You should be able do this inside or outside of Mythtv.
Inside of mythtv, in the backend setup, set up a Video Source with no grabber. Call it "conversion" or whatever. In Input Connections, bind this Video Source to the unused Composite input of your card.
In Channel Editor, go to this "Conversion" video source and add a channel to it. Give the a number, say "3" or "4" Mark the channel as "invisible" (because you don't need it to appear in your schedules listings) Go back into Input Connections and set this channel as the startup channel in preference to "Please add" for this composite input. Exit.
Now you should be able to Manual Schedule recording through this input, as though it were an odd sort of VCR, or you can run it in LiveTV and watch what it's cranking in by changing LiveTV to the "conversion" Video Source by means of the on-screen "m" key menu when you've entered LiveTV. After your LiveTV "show" is complete, you go into the AutoExpire list and move this livetv recording into the Default group, where it becomes permanent and can be trimmed, edited, and transcoded like any other Mythtv recording.
Outside Mythtv, I suppose you'd use v4l-utils to control the Composite input of your card directly (if this card has been set up in Mythtv with "open dvb on demand", so Mythtv releases it when not in use, and the card is not otherwise engaged in a recording).
would likely list all the card's inputs. (or the number listed for the composite input) would likely change this to the Composite input. Then,
...or whatever /dev/videoX number the device is on, should produce playable recording "video.mpg" from whatever's coming in through the card's analog tuner.
cat /dev/video0 > video.mpg