How does take off mass impact induced drag?
Induced drag is caused by lift. (historically, Induced Drag was named "lift induced drag").

If weight(mass) of the aircraft decreases, the lift required to fly the aircraft decreases. And the drag associated to that lift also decreases.

The quoted statement is true, but "slightly" can be discussed. Because the increase in range depends a lot on how much payload the aircraft could carry. (If it's %50 of the max takeoff weight, the range could increase a lot).