In this paper, the η-Nash equilibrium (η-NE) region of the two-user linear deterministic interference channel (IC) with noisy channel-output feedback is characterized for all η > 0. The η-NE region, a subset of the capacity region, contains the set of all achievable information rate pairs that are stable in the sense of an η-NE. More specifically, given an η-NE coding scheme, there does not exist an alternative coding scheme for either transmitter-receiver pair that increases the individual rate by more than η bits per channel use. Existing results such as the η-NE region of the linear deterministic IC without feedback and with perfect output feedback are obtained as particular cases of the result presented in this paper.