One of the methods to analyse the ITZ is to do petrographic examination of specimen prepared from cement mortar used.
Please refer literature related to petrographic examination.
You need to prepared slices from materials and do the examination by scanning electron microscope (SEM) or other suitable microscope depending upon your requirement.
Carrying out SEM on the cross section of your sample will give you details about the effect of the waste marble powder on the ITZ. You might want to compare your result with the SEM of samples containing only cement as binder (i.e. control)
I'm assuming you want to know the size of the ITZ, in which case petrography or SEM analysis would be best.
The book "A Practical Guide to Microstructural Analysis of Cementitious Materials", CRC Press, 1st Edition, by Karen Scrivener, Ruben Snellings and Barbara Lothenbach gives a very good overview of SEM analysis.
You can analyse the ITZ using Microhardness test, SEM analyis in the backscatter mode, and EDS line analysis. The details of these methods can be found here:
Influence of the surface roughness of crushed natural aggregates on the microhardness of the interfacial transition zone of concrete with mineral admixtures and polymer latex