Despite the advanced capabilities of contemporary machine learning (ML) models, they remain vulnerable to adversarial and backdoor attacks. This vulnerability is particularly concerning in real-world deployments, where compromised models may exhibit unpredictable behavior in critical scenarios. Such risks are heightened by the prevalent practice of collecting massive, internet-sourced datasets for pre-training multimodal models, as these datasets may harbor backdoors. Various techniques have been proposed to mitigate the effects of backdooring in these models such as CleanCLIP which is the current state-of-the-art approach. In this work, we demonstrate that the efficacy of CleanCLIP in mitigating backdoors is highly dependent on the particular objective used during model pre-training. We observe that stronger pre-training objectives correlate with harder to remove backdoors behaviors. We show this by training multimodal models on two large datasets consisting of 3 million (CC3M) and 6 million (CC6M) datapoints, under various pre-training objectives, followed by poison removal using CleanCLIP. We find that CleanCLIP is ineffective when stronger pre-training objectives are used, even with extensive hyperparameter tuning. Our findings underscore critical considerations for ML practitioners who pre-train models using large-scale web-curated data and are concerned about potential backdoor threats. Notably, our results suggest that simpler pre-training objectives are more amenable to effective backdoor removal. This insight is pivotal for practitioners seeking to balance the trade-offs between using stronger pre-training objectives and security against backdoor attacks.