Difficult!
I would say however, you are familiar with carpet moth (my sympathies!) but are you familiar with Persian rugs? Many old ones show signs of old damage, long dealt with.
If you don't know her well enough to guess at her reaction, then I think best to say nothing.
However, 2 possibilities:
Do you have a mutual friend that you could mention it to? Say you are happy (moth survivor) to have a word but didn't want to intrude, and see if friend can guide you.
Could you, on next meeting, have a conversation about Persian rugs? "they are so beautiful, but I don't know much about them..."
I have to say that unless a person (or sometimes an animal) is at risk, I tend towards saying nothing.