Is it possible to produce hydrogen sulfide with tap water and activated carbon or CuZn?

Please note I'm a bit out of my depth with chemistry.


**The situation:**
I have a [KDF](http://www.kdfft.com/HowItWorks.htm)/GAC water filter that defies logic and releases $\ce{H2S}$ (assuming it by smell/taste) in the water after filtration.


Is it possible that some reaction could produce $\ce{H2S}$ with water and $\ce{CuZn}$ media (such as [KDF](http://www.kdfft.com/HowItWorks.htm)) or GAC (Granulized Activated Carbon).


The more practical problem:
[DIY Exchange - KDF Filter Question](https://diy.stackexchange.com/questions/133418/why-does-a-new-kdf-gac-filter-cause-a-rotten-egg-smell-taste)


