My question is if I respond to the woman's threat of legal action against me by contacting her via email/mail, can she use my response against me in court?
While any person can sue another person for anything, not all suits are well founded in fact under current law or a good faith extension of current law. Such suits are frivolous.
Under the facts above, THERE CAN BE NO VALID LAW SUIT FILED AGAINST YOU. But a Frivolous one could be filed. I personally would not worry about it.
"Though, I don't know if I should just reach out to her directly and attempt to diffuse the situation"
The is a personal Opinion - not so much a legal answer
Exactly what I would do. My opinion, always be the nice guy, not for others, but for yourself. It is really great to look back and see all the good deeds you have done especially for people who acted badly and did not deserve them.
So under your facts, I would make it clear to this person you owe her nothing. And if she does not believe you, tell her to just ask a lawyer.
Then give her some photos if the work is already done and it is no or little extra costs to you.
When you look back years from now you will be glad you did. You reap what you sow in this world.
Not a legal position just a personal philosophy from someone who has to deal with people acting badly every day.