Demagnetization of pulse transformer megnetizing inductance
If you concentrate on the magnetising current Ilm, the algebraic sum of primary and secondary current, then to first order, Ilm rises linearly during the on time due to the constant applied 3 V, as dI/dt = V/L. The main departure from linearity is due to the finite resistance of the primary. As the current increases, the voltage drop across this resistance reduces the available voltage for ramping Ilm, and the current rises more slowly later on in the pulse.

In the off time, the way Ilm falls is down to how you choose to reset the magnetisation in the core. You choose what voltage to apply, and the current will change accordingly. You can apply a voltage by letting the core drive current through a resistor, or a zener, or you can switch to a voltage source. Many people opt for a zener as (1) it's passive, so the current stops at zero (unlike switching to a specific voltage) and (2) it's faster than a resistor for the same peak voltage, as the voltage doesn't drop by much as the current falls. 

Choose a flux reset voltage value so you reach zero current before the next pulse, under your worst case duty cycle conditions. It doesn't matter whether you reset the flux very quickly and spend a while at zero, or only just get to zero before the next pulse begins.