In this paper we examine the value of feedback that comes from overhearing, without dedicated feedback resources. We focus on a simple model for this purpose: a deterministic two-hop interference channel, where feedback comes from overhearing the forward-links. A new aspect brought by this setup is the dual-role of the relay signal. While the relay signal needs to convey the source message to its corresponding destination, it can also provide a feedback signal which can potentially increase the capacity of the first hop. We derive inner and outer bounds on the sum capacity which match for a large range of the parameter values. Our results identify the parameter ranges where overhearing can provide non-negative capacity gain and can even achieve the performance with dedicated-feedback resources. The results also provide insights into which transmissions are most useful to overhear.