How the effect of the output inductor is minimized and filter offers only single pole by current mode control?
With voltage mode control you have a control system measuring the output voltage and modifying a PWM signal feeding an LC filter.  So you have the double pole response of the filter inside the loop to compensate.

With current mode control you have an inner current loop.  It senses the inductor current (with a resistor in series, or by other methods) and changes the duty cycle of the power stage to keep the current proportional to a control voltage, making it a voltage-controlled current source. (Within BW limits, etc.)

So the outer voltage loop "programs" the current loop, which typically has a higher bandwidth than the voltage loop.

To the outer control loop this "looks" like a voltage controlled current source driving a load capacitor, which is a single pole response.  So compensation of the outer loop is easier, typically done with a type II compensator vs. the type III compensator necessary for voltage mode control.