From what I understand LLMs are just large heuristic machines. They gather a lot of statistics on token order and return an answer to that with something that statistically should higher than other options. There's no "understanding". So to answer your question, no, they don't understand the license.

Content is most likely scraped wholesale from websites, possibly run through some clean up to possibly filter out absolute garbage, and fed into an LLM to train it. An LLM can be tricked to reveal its training data (e.g repeat "fruit" forever). It's in those cases where copyright infringement is detected and if action can and has be taken. There are court cases currently in review, the most popular being the one against Github Copilot for infringing on the license of sourcecode it ingested.

Anti Commercial-AI license