Hello there! What an interesting and somewhat challenging question!
First, let's talk a little about probiotics. Probiotics, as defined by the World Health Organization, are "live microorganisms which when administered in adequate amounts confer a healthy benefit to the host." What that means is that it's the healthy microorganisms found in yogurt, kimchi, fermented mustard leaf, and sauerkraut, to name a few, that are good for your gut. The key here is that these microorganisms are live.
There are studies that suggest that probiotics are good for digestion, for diarrhea and a few other illnesses. However, there are hundreds (maybe millions!) of different strains of probiotics that research is still a bit unclear which strains can help.
Which leads me to your question! There is research that says that probiotics are only useful when they are live, which means killing them with heat may not show any health benefit. However, I could not find at what specific temperature would kill the probiotics.
So, if you are just warming up the fermented mustard leaf, you may or may not kill the probiotics. However, if you are cooking with it on high heat, unfortunately, I am unsure if the probiotics would still be beneficial.
Hope that helps!