Multimodal sarcasm detection is challenging, especially in low-resource settings where subtle image-text contradictions are hard to learn due to scarce annotated data, which hinders the model's performance. Parameter-efficient fine-tuning (PEFT) methods like adapters, LoRA, and prompt tuning reduce overfitting but struggle to reach optimal performance due to limited supervision from few-shot data. We propose PEKD, a unified framework that enhances PEFT methods via distillation from an expert model trained on large-scale sarcasm data, which acts as the teacher. To mitigate unreliable signals from the teacher, we introduce an entropy-aware gating mechanism that dynamically adjusts the distillation strength based on teacher confidence. Experiments on two public datasets demonstrate that our PEKD framework enables PEFT methods to outperform both prior parameter-efficient approaches and large multimodal models, achieving strong results in the few-shot scenario. The framework is modular and adaptable to a wide range of multimodal models and tasks.