If it is not possible to get this information, could you point out the code snippet that performs the rectification step? Since GDAL's code base is quite large, it is not easy to find the appropriate location.
Entry point of the logic to compute the transformation from source pixel coordinates to target pixel coordinates

https://github.com/OSGeo/gdal/blob/master/gdal/alg/gdaltransformer.cpp#L1380

And in the first step of this transformation, when using polynomial adjustment of GCPs, you'll use:

https://github.com/OSGeo/gdal/blob/master/gdal/alg/gdal_crs.cpp

Even

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