As large language models (LLMs) grow in parameter size and capabilities, such as interaction through prompting, they open up new ways of interfacing with automatic speech recognition (ASR) systems beyond rescoring n-best lists. This work investigates post-hoc correction of ASR transcripts with LLMs. To avoid introducing errors into likely accurate transcripts, we propose a range of confidence-based filtering methods. Our results indicate that this can improve the performance of less competitive ASR systems.