Recent studies have demonstrated the lack of robustness of image reconstruction networks to test-time evasion attacks, posing security risks and potential for misdiagnoses. In this paper, we evaluate how vulnerable such networks are to training-time poisoning attacks for the first time. In contrast to image classification, we find that trigger-embedded basic backdoor attacks on these models executed using heuristics lead to poor attack performance. Thus, it is non-trivial to generate backdoor attacks for image reconstruction. To tackle the problem, we propose a bi-level optimization (BLO)-based attack generation method and investigate its effectiveness on image reconstruction. We show that BLO-generated back-door attacks can yield a significant improvement over the heuristics-based attack strategy.