My local git repository is on a Linux, on a vmware.
I want to know which file had been modified (Or which file is new), and controlling these events through GUI-tools.>
you could use any GUI which uses git commandline (which is NOT TortoiseGit, but for example gitextensions, sourcetree, gitgui&gitk) and make it use instead of real Git a script which transparently runs each command at the remote system.
https://github.com/ericpruitt/sshfsexec is an example of such approach.