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Multi-Modal Large Language Models (MLLMs) have exhibited remarkable performance on various vision-language tasks such as Visual Question Answering (VQA). Despite accumulating evidence of privacy concerns associated with task-relevant content, it remains unclear whether MLLMs inadvertently memorize private content that is entirely irrelevant to the training tasks. In this paper, we investigate how randomly generated task-irrelevant private content can become spuriously correlated with downstream objectives due to partial mini-batch training dynamics, thus causing inadvertent memorization. Concretely, we randomly generate task-irrelevant watermarks into VQA fine-tuning images at varying probabilities and propose a novel probing framework to determine whether MLLMs have inadvertently encoded such content. Our experiments reveal that MLLMs exhibit notably different training behaviors in partial mini-batch settings with task-irrelevant watermarks embedded. Furthermore, through layer-wise probing, we demonstrate that MLLMs trigger distinct representational patterns when encountering previously seen task-irrelevant knowledge, even if this knowledge does not influence their output during prompting. Our code is available at https://github.com/illusionhi/ProbingPrivacy.