We model transportation networks as dynamic graphs and introduce the ability for agents to use Backward Time-Travel (BTT) devices at any node to travel back in time, subject to certain constraints and fees, before resuming their journey. We propose exact algorithms to compute travel plans with constraints on BTT cost or the maximum time that can be traveled back while minimizing travel delay (the difference between arrival and starting times). These algorithms run in polynomial time. We also study the impact of BTT device pricing policies on the computation of travel plans with respect to delay and cost and identify necessary properties for pricing policies to enable such computation.