The spread of climate-related misinformation can reduce public support for climate change mitigation policies. A study showed that on social media, people tend to absorb news content without knowing the details of the context. In that case, LLM can be utilised to spread misinformation, subsequently altering people's opinions for malicious purposes. To observe two machine learning algorithms: Support Vector Machine and Logistic Regression's capability to detect LLM-generated misinformation, we created a synthetic dataset, consisting of 300 examples. We have collected 150 climate-related news articles from various well-reputed sources to create the synthetic dataset. Then, we created a five to six-sentence summary based on the original article with the help of GPT-4. Each actual summary is falsified with the help of GPT-4 as well. Moreover, we evaluated each summary example from the synthetic dataset with the FineSure framework to obtain each summary's faithfulness, completeness and conciseness. The results showed that Support Vector Machine achieved an F1-score of 0.839, and Logistic Regression's F1-score was 0.787 on the synthetic dataset. We performed sentence-level analysis with the GUTEK framework on these models' false positive and negative examples. The sentence-level analysis with the GUTEK framework showed that policy-related sentences had the most impact on these models in predicting false positives. On the other hand, factual-related sentences significantly influenced these models to predict false negatives.