Mechanically, there's one really good option in the 2e rules, though it isn't exactly its main purpose: Possession. While in a host:
The entity may pay one Essence per turn to heal a lethal or
bashing wound or a point of structure lost to damage.
Now in 1e, there was a Numen, Heal, which does what you want. It's in Book of Spirits. Regenerate also happened to be in the same book, and though Regenerate was imported unmodified into GMC and 2e core, Heal was not. Also unlike Regenerate, Heal could remove aggravated damage at the cost of only some extra Essence, so it's possible it was left out of 2e for a reason.
• Heal: The spirit can heal others’ wounds, typically for a hefty price. The spirit expends a point of
Essence and rolls Power + Finesse. Bashing damage
is healed before lethal, and all lethal damage must be
healed before aggravated damage. Each success heals a
level of bashing damage, while two successes can heal a
point of lethal damage. The lethal damage healed can
be used to mend aggravated damage, but each point of
aggravated damage cured costs one additional point of
Essence. (Healing two aggravated wounds calls for four
successes and three points of Essence.) This Numen
may also be used to help a character fight off disease
or the effects of poison — each success adding to the
character’s resistance rolls on a one-to-one basis.
On the other hand, Influences causing healing seems sort of plausible, but there's a problem. It's extremely unclear how applying e.g Influence: Healing would work in practice, because an Influence is almost always a temporary effect, and healing wounds would be a permanent one.
Influence is measured in both scale and duration. To use
an Influence, compare the entity’s Influence rating to the
total dots of the intended effect and how long it is to last.
The total must be equal to or less than the entity’s Influence
rating in order for the Influence to be attempted.
In the description of Influence Effects:
• Strengthen The entity can enhance its sphere of influence. It can add to the Defense of a loved
one, make an emotion stronger, an animal or plant healthier, or an object more
robust, gaining the entity’s Rank in Health or Structure.
When it says it can make an animal "healthier," in context it means the same thing as when it says it can make an object "more robust": it strengthens them by making them temporarily harder to kill, it doesn't reverse damage. An entity with Influence: Dogs ••• can use Strengthen on a dog, to give it temporary Health dots equal to its Rank, raising the dog's maximum health, but only for a limited duration. One with Influence: Cars ••• could give a car temporary extra Structure, which is the equivalent of Health for objects, making it more robust and harder to destroy.
Now a powerful Rank 5 angel might be able to have 5 dots of Influence, which would allow it to use a Strengthen • effect with a Permanent •••• duration. The RAW only suggests this could do things like permanently increase a target's maximum Health, but permanently removing a wound could be argued as an extension of that.
For Influences less overwhelmingly powerful than 5 dots, you'd have to make up a houserule. Maybe Influence: Healing could temporarily accelerate (you'd have to decide by what factor. Maybe multiply by Rank+1?) the target's natural healing rate, assuming they can heal naturally and aren't undead. But to make the effect last longer than mere minutes, which is useless for anything but healing bashing damage, consult the Influence Durations table:
•• | One hour per success
••• | One day per success
It would need 3 or 4 dots of Influence: Healing in order to have any practical effect, because for humans lethal damage takes two days to heal. A Rank 3 entity with 3 dots of Influence might, with 6 successes, make the next 6 hours of time count as 24 hours towards healing a single point of damage, and a Rank 4 entity with 4 dots would let a human heal one point of lethal damage every 10 hours or so, for however many days its influence lasts. Alternatively, if you made the acceleration factor "Rank times 10," a Rank 3 entity could reasonably cause lethal wounds to heal in less than 2 hours each.
Incidentally, there is a story told in Mortal Remains about an angel healing a permanent injury, effectively a persistent Arm Wrack Condition, of the founder of the demon-hunting conspiracy the Knights of Saint Adrian, but it was done as part of granting their Endowment, Ink.
The target was
an enemy of God. Then he paused,
and asked if Casey could track him
down. She said sure, but somebody else would have to strangle
the guy. And that was when the
angel healed her arm, no price
The angel who fixed up Casey Howard’s arm did it by tattooing her in some weird script. It looks a bit arcane, a little
high tech. Every so often, he comes by to outfit the new hires
with Ink, holy marks that help in the endless hunt for his fallen
Casey Howard’s original Ink healed a serious injury. This is the
type of thing the Storytelling system doesn’t usually model, so the
Ink Endowment doesn’t include an option for a tattoo that heals
an individual injury.
That said, a character being grievously and permanently
wounded is the kind of thing that might happen with a persistent
Condition. Optionally, the client might be willing to patch up a
seriously hurt hunter. That hunter would have to be pretty valuable
to the agency (as represented by two or more status dots) to be
worth the client’s time.