I agree the tech quiz should get you back into the books for some relevant and important stuff and not trying to steal people's time with useless nonsense.
And yes, in certain scenarios a reduced thrust can increase your RTOW. Remember V1 is basically limited by 2 factors: 1. VR and 2. VMCG. Now if the runway is contaminated and my V1 is on the lower limit because of VMCG but yet I'm not able to stop on the remaining RWY, I have to lower my V1. But yet I can't do that because of the lower limit is VMCG so only solution is to lower thrust and thus decrease VMCG speeds.
So the problem here is not the get airborne but to stop on a contaminated RWY.