We present a Multimodal Backdoor Defense technique TIJO (Trigger Inversion using Joint Optimization). Recent work https://arxiv.org/abs/2112.07668 has demonstrated successful backdoor attacks on multimodal models for the Visual Question Answering task. Their dual-key backdoor trigger is split across two modalities (image and text), such that the backdoor is activated if and only if the trigger is present in both modalities. We propose TIJO that defends against dual-key attacks through a joint optimization that reverse-engineers the trigger in both the image and text modalities. This joint optimization is challenging in multimodal models due to the disconnected nature of the visual pipeline which consists of an offline feature extractor, whose output is then fused with the text using a fusion module. The key insight enabling the joint optimization in TIJO is that the trigger inversion needs to be carried out in the object detection box feature space as opposed to the pixel space. We demonstrate the effectiveness of our method on the TrojVQA benchmark, where TIJO improves upon the state-of-the-art unimodal methods from an AUC of 0.6 to 0.92 on multimodal dual-key backdoors. Furthermore, our method also improves upon the unimodal baselines on unimodal backdoors. We present ablation studies and qualitative results to provide insights into our algorithm such as the critical importance of overlaying the inverted feature triggers on all visual features during trigger inversion. The prototype implementation of TIJO is available at https://github.com/SRI-CSL/TIJO.