You have two choices:
1. Install git on your LINYX machine, which you probably can't do if it's a pure NAS outside of your control.
2. Run everything off Windows as git in local mode. Mount the NAS as a windows drive. In a command terminal:
a. cd X:\Share\repo.git #you'll have to mkdir this
b. git init --bare #creates a new empty repo on your NAS
c. cd C:\MyStuff #where you keep your clones
d. git clone -l X:\Share\repo.git #clone the bare repository
e. Start adding stuff (git add, git commit)
f. git push # to move commits to your NAS repo.
Then you have your relationship and can push/pull from your NAS entirely from within Windows executing objects. Change directories and drive letters accordingly. -l means local, so git won't be starting any git-upload-pack processes remotely. Variations on this should work.
Good luck.
Randall