I also asked the pharmacist and they said to dispose of the pen in the sharps container. Also have asked about what to do with the sharps container when full. I asked both pharmacy and local landfill on correct procedure for my area to dispose of the sharps container with pens. I was told to use packing tape to secure the container and sharpie to mark the outside with the words "do not recycle" then dispose of in the regular trash. So that's what I've done since starting. I can get about 6 months of pens and needles in a 1 quart container.

I suggest you call your local waste disposal agency and also your local pharmacy for what is appropriate for your principality and state.