We show that terahertz (THz) emission spectroscopy is a method to probe the in-plane magnetic state in spintronic heterostructures with exchange bias between the constituent antiferromagnetic and ferromagnetic layers. We demonstrate that the intense laser excitation can switch and reversibly reset the direction of the pinning axis arising from the exchange bias in technologically relevant tunnel magnetoresistance elements. By applying the double-pump THz emission spectroscopy, we reveal that this switching exhibits a threshold character in the pump intensity.