According to Dorothy, the Key to Oz works in any door (emphasis mine):
Dorothy: It's the key to Oz. There are magical ways into Oz - tornado, eye of a hurricane, whirlpool - but this key will turn any locked door into a portal to Oz. Insert key, twist, and presto, you're in Oz.
Supernatural Season 9 episode 4 "Slumber Party"
How this works when going from Oz to our world is never discussed, but presumably it works similarly.
The quote above indicates that there are ways into Oz that don't require the key, which presumably means there are other ways out of Oz as well. "Slumber Party" makes a point of saying that the Ruby Slippers don't work that way, but the Wizard of Oz in "There's No Place Like Home" appears to use a spell that transports him from Oz to any location in our world, and he presumably had a plan to get back1:
Good!Clive Darrow: Without the key to Oz there's no way we can get back to the Wizard, but there may well be a way to summon him here. If I am mortally wounded, he'll have to come back here to save us both.
Supernatural Season 10 episode 11 "There's No Place Like Home"
If the Wizard knew this spell, it's possible that any surviving Good Witches could have known it as well.
The Charlies could have used any of these means to get out of Oz, or she could have used the key and broken it once on this side. The episode doesn't specify, so barring future information it's all speculation.
1 No word on how the Wicked Witch didn't know this spell