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The success of modern multimodal representation learning relies on internet-scale datasets. Due to the low quality of a large fraction of raw web data, data curation has become a critical step in the training pipeline. Filtering using a trained model (i.e., teacher-based filtering) has emerged as a successful solution, leveraging a pre-trained model to compute quality scores. To explain the empirical success of teacher-based filtering, we characterize the performance of filtered contrastive learning under the standard bimodal data generation model. Denoting $\eta\in(0,1]$ as the fraction of data with correctly matched modalities among $n$ paired samples, we utilize a linear contrastive learning setup to show a provable benefit of data filtering: $(i)$ the error without filtering is upper and lower bounded by $\frac{1}{\eta \sqrt{n}}$, and $(ii)$ the error with teacher-based filtering is upper bounded by $\frac{1}{\sqrt{\eta n}}$ in the large $\eta$ regime, and by $\frac{1}{\sqrt{n}}$ in the small $\eta$ regime.