Machine unlearning is widely used to remove hazardous knowledge from large language models. Modern Vision-Language Models (VLMs), however, process both text and visual inputs, raising a fundamental security question: does unlearning in one modality transfer to the other? We present the first systematic, bidirectional study of cross-modal unlearning transfer across three VLM architectures: LLaVA-1.5 (MLP projection), InstructBLIP (Q-Former), and IDEFICS (gated cross-attention). We find that unlearning transfers across modalities, but the transfer is asymmetric and incomplete. In some cases, text unlearning strongly transfers to vision. However, this robustness is not preserved under typographic attacks that manipulate the visual presentation of text. Under such attacks, previously unlearned knowledge can be readily recovered, indicating shallow unlearning. To address the transfer gap and shallow robustness, we propose \textsc{CrossInf}, an influence-guided mitigation strategy. Motivated by the observation that different model components contribute unequally to cross-modal transfer, \textsc{CrossInf} focuses unlearning on transformer blocks that most influence cross-modal generalization. It reduces the transfer gap by more than half in architectures with strong fusion, while preserving model utility. It also improves robustness under typographic attacks, reducing the attack success rate to near zero. We further conduct human evaluation with three annotators ($κ{=}0.77$) to validate our findings. Finally, we analyze shallow unlearning using Centered Kernel Alignment (CKA), providing insights into the observed transfer behavior and robustness limitations.

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