Why does the pulse shape of my scope probe compensation look different from the pulse shape shown…

The compensation signal (square wave) that you see is different from the pulse shape shown in the U1602A/U1604A's user’s manual because of the additional 10 MΩ series resistor between the signal source and the BNC output. With the 10 MΩ impedance, the rise time of the square wave is increased. The 10 MΩ impedance is an additional safety feature to provide an extra 300V CAT III isolation protection.

See the graphics below as a reference of the pulse shape for scope probe compensation.