I'm not sure what the preferred method is for removing the mouthpiece safely, but I noted that the first time I removed mine that it would not fit snuggly afterward.
Looking a little closer there are tiny pieces on the end of the mouthpiece that look like they clip it in place once inserted. One of mine had broken off and now it falls out easily if I'm not careful. It may be that to remove it you need to pull straight out instead of trying to wiggle it out from side to side while pulling.
I'm still waiting to see when they will be available to order from the website.
The mouthpiece does click back into place if you put it in one side at a time. The Firefly user manual has photos along with instructions: