The word would be patroness.
Matron implies dedication, yes, but also describes the entity rather than the relationship. Grr, the English language.
As I said, if it's Amber's personal gnosis that Artemis is so-and-so way and wants her to do this, that, or the other...then it is.
Some deities demand periods of fasting, or some vow of silence, or veiling...some kind of separation from some aspect of the world. I think the Eleusian Mysteries had some religious rites that were reserved for women only (which didn't stop this one Athenian guy from disguising as a woman to join in on this and then becoming this minor god of marriages...fun story. His name was Hymen.)
So, I can kind of understand some divine mandate or other to separate from whatever. But I don't know... is this personal gnosis? Or is it gender prejudice justified by religion.
Either way, Amber did say please, so as much shade as I've been throwing on the reasoning, I ought to support and respect that personal boundary that she's set out.