Best way to add environment variables to MobaXterm
In the "Terminal tab settings" section, so you will find this option in the "Terminal" tab.
Go to MobaXterm global settings window, then click on the "Terminal" tab and check the "Use Windows PATH environment". Note that if you are using a session, you will have to do the same in this session: edit your session, then go to the "Terminal settings" tab and check the "Use Windows PATH" option.
I had the same issues while trying to use git. It looks like MobaXterm keeps using his own executables located %USERPROFILE%\Documents\MobaXterm\slash\etc, and even recreates them when you delete them.
You can still force MobaXterm to use windows PATH configurated executables by launching cmd /c yourcommand, in my case cmd /c git push. It will run windows CMD command using your PATH environment variable.
You have to check "Use Windows PATH" on the "Terminal settings" of your MobaXterm session settings in order to works.