Wormhole X-treme is currently one of the more popular missions among players, with text making each obstacle cost power +1 to play. Well, Gairwyn is almost like having that mission in character form. Despite the fact she only offers 1 Ingenuity, skill-wise, she remains a very cheap way to make it harder for your opponent to defend against you.

She's also incredibly flexible -- just because her only skill is Ingenuity doesn't necessarily mean the best time to play her is during an Ingenuity mission. Most decks have 1 or 2 skills they're "good" at, and another skill they're only "average" at. Playing Gairwyn as your first action when you've just played a mission of that "average" skill can mean the difference between success and failure. You may only have, say, 5 Culture to assign to that 3 Culture mission, but with a just-played Gairwyn to drive back the obstacles a bit, that might just be enough.
Of course, Gairwyn's text -- no matter how useful -- works for only a single mission. Which puts her in the interesting position of being a support character you might not mind having destroyed. So remember, you're the one who chooses the "dead character" when your opponent revives Anubis, Banished Lord. Investigate Disappearance might be a good mission for a deck with 3 Gairwyns. Or, if you want to take a more active approach, you might try also putting Harlan in your Gairwyn deck.
By using Harlan to play Gairwyn (whether you actually have a copy of Gairwyn in play or not), you can ensure that Gairwyn will be destroyed at the end of your turn, clearing the way to play another next turn.