I also hear this and have heard similar things with other letters in other lessons. I have the idea (don't know where I got it) that in Czech, ALL letters are pronounced. So now I'm thinking that what we're hearing is the effect of each M being pronounced independently-- as opposed to the two Ms being run together into a single sound.
If a native speaker could weigh in on this, that would be great.
My inference from what I've learned so far is that c before h is never pronounced.
C before H constitute together a single separate letter CH (it has its own place in the alphabet). It is pronounce differently from H, higher in the throat.
CH is pronounced similarly as in German and some other languages. The sound is missing in English but it exists in Scots (e.g., loch https://cs.forvo.com/word/loch/#sco ). Hear it in https://cs.forvo.com/word/chacha%21/#cs
Read more about Czech pronunciation in the Tips and Notes.
I have a hard time imagining this sentence coming up in general conversation. Perhaps in a game?