for(int I = 0; I < 4; ++I) {
        real32 PixelPx = (real32)(XI + I);
        real32 PixelPy = (real32)Y;
        real32 dx = PixelPx - Origin.x;
        real32 dy = PixelPy - Origin.y;
  
        real32 U = dx*nXAxis.x + dy*nXAxis.y;
        real32 V = dx*nYAxis.x + dy*nYAxis.y;
  
        //rest of the loop
  }

  real32 PixelPy = (real32)Y;
  real32 dy = PixelPy - Origin.y;
  
  real32 PixelPx = (real32)(XI);
  real32 dx = PixelPx - Origin.x;
  
  real32 U = dx*nXAxis.x + dy*nXAxis.y;
  real32 V = dx*nYAxis.x + dy*nYAxis.y;
  
  for(int I = 0; I < 4; ++I) {
      U += nXAxis.x;
      V += nYAxis.x;
      
      //rest of the loop
  }

This also results in the subexpression dynXAxis.y and dynYAxis.y being lifted outside the loop.

Now we've moved half of the code outside the loop but we aren't done yet.

The same can be done with PixelPx and dx, the trick is to then replace dxnXAxis.x with

  (dx + I)*nXAxis.x

  (dx + I)*nXAxis.x

  dx*nXAxis.x + I*nXAxis.x

  dx*nXAxis.x

  I*nXAxis.x

  U += nXAxis.x