An increasingly common practice is to train large language models (LLMs) using synthetic data. Often this synthetic data is produced by the same or similar LLMs as those it is being used to train. This raises the question of whether the synthetic data might in fact exacerbate certain "blindspots" by reinforcing heuristics that the LLM already encodes. In this paper, we conduct simulated experiments on the natural language inference (NLI) task with Llama-2-7B-hf models. We use MultiNLI as the general task and HANS, a targeted evaluation set designed to measure the presence of specific heuristic strategies for NLI, as our "blindspot" task. Our goal is to determine whether performance disparities between the general and blind spot tasks emerge. Our results indicate that synthetic data does not reinforce blindspots in the way we expected. Specifically, we see that, while fine-tuning with synthetic data doesn't necessarily reduce the use of the heuristic, it also does not make it worse as we hypothesized.