Build Delta Package with Teamcity

hi Guys, 

I´m quite new with Teamcity, so apologize if wording is quite "amateurish". For our project (a datawarehouse) we use bitbucket as repository.
Now we want to automate the build of the weekly deployment packages and got told to use teamcity.

Our deployment "container" is a delivery.zip which contains only the changed files to the existing production code, (kind of delta deployment).
The zip-File is then transported to the target machine for automated deployment. (This part of the process is already in place). 

So, we have started with teamcity and managed to generate an output zip based on  our release branch .
But this package contains the full branch. What we need is  an output.zip. containing only the changed files to the master branch instead .
I have tried for some days now, made some progress to get a list of the changed files using git diff in a command line build step,

But have still no idea how I can extract those changed files in another zip. Would really be great if you could give me some hints to get back on track.
Thanks in advance.