To be honest, I'm not comfortable with an Aegis blowing down, or even suppressing, Parma Magica under any circumstances. Parma is described as "an Ability that grants magic resistance that adds to the resistance arising from a maga's Form scores." It's not described as a Spell, or even a spell-like ability. It's something that seems to be a breakthrough that has yet to be properly explained by, let alone fit into, proper Hermetic theories.
The things that the description of Aegis of the Hearth says it protects against:
- Any spell cast toward the Aegis (originating from outside it) by any magus not involved in the ritual. Parma is not a spell and only affects the casting magus, so that's not it.
- Spells that bring objects into the Aegis. The Parma doesn't bring anything into the Aegis, so that's not it.
- If a foreign spell cannot penetrate a resistance equal to the level of the Aegis, it fizzles out. Again, not a spell, so this doesn't apply.
- Foreign Intellego spells (even those that can't be blocked by Parma Magica). Not Intellego in any way, so it doesn't apply.
- Spells that were cast before they entered the Aegis, such as an invisibility spell cast on a magus outside the Aegis. I think this is the closest thing to what Arya's saying, but again, this only applies if you rewrite the Parma Magica to be a Rego Vim spell as Arya seems to have done. However, the rules as written say that it's an Ability which is described as a Ritual that takes two minutes to perform, not as a Ritual Spell that takes two minutes to cast. My understanding of the rules as written lead me to believe that this provision doesn't apply, either.
- Spells cast within the Aegis by magi who were not involved in the casting of the Aegis subtract half the Aegis's level from their Casting Total. Unless you're performing your Parma Ritual within the Aegis, this wouldn't apply. And if you were, it would only apply if you rewrite Parma Magica as a spell.
- Effects from an Enchanted Device. You can't instill Parma Magica in a device, so that doesn't apply.
- Creatures with a Might Score can't enter unless their Might is higher than the Level of the Aegis. Magi don't have a Might score, so this doesn't apply.
Of the eight effects of the Aegis listed, only two could conceivably apply, and even then, only if you completely rewrite the Parma Magica. Doing so, I think, would effectively cripple the Order. Instead of (as the Aegis description states), feeling a slight tingling in the extremities when approaching the border of the Aegis, the first sign a Magus would have that they're approaching a covenant would most likely be the collapse of their Parma (unless you interpret "approaching the border" to indicate a warning zone, perhaps a pace wide, along the boundary).
Having Aegis quash the Parma would result in very few magi ever leaving their covenant for any reason, unless they knew for certain that their path to the other covenant would not cross another covenant's boundary, and unless they knew for certain that they would not only be given casting tokens at their destination but that they would not be un-invited as the Gallus Florensians were.
Even the effects of Winds of Mundane Silence aren't limited to spells and Parma Magica; if it were, then I could see a tenuous link to this and the Aegis effects we've just discovered in this saga. However, the spell description and the Guideline both say that it applies to any magical effect, not simply spells.
So, in a nutshell, my opinion/belief is that Aegis of the Hearth has no affect on Parma Magica whatsoever. I could conceivably make an argument that, if you are within a foreign Parma without a casting token at sunrise or sundown and need to renew your Parma, you would make a Stamina + Parma Magica roll against an Ease Factor of (3 + magnitude of the Aegis), just like a transformation roll for Bjornaer, which actually makes perfect sense to me.
It smells like roses, too!