Need more info to expand, but this might get some ideas going, and much depends if this is simply a side venture or meant to become something more in your campaign.
A) Mythology Route: The Banshee heralds imminent death of a particular bloodline with her singing, and the party's efforts to liberate her will have no significance as she's singular in existence and purpose (not all dead want to be set to rest). If you haven't revealed anything more than there's bones of a long-dead elf female, you could add to the story through ancient clues, a picture here and a faded diary there. Let's say the elf, Ellie, never cried as a child, and neither did her mother, and Ellie was never allowed to sing, being punished if she even asked. Her mother always believed the two of them to be of Banshee blood (even if she didnt' know the word for it) and you could have a letter from mother to daughter explaining this, that mother entered a room and screamed out (a surprise to her as the sound was spontaneously ripped from her mouth). Others in the room stood horrified. The next day, someone in that room unexpectedly died. She then cites a time as a baby Ellie screamed out, an unholy scream from some other realm, as an elderly nurse entered to take care of her. The nurse fled the room and died later that day, taking a nasty fall. It could be an apology letter for never letting Ellie cry or sing, for the belief was that in their blood lay the power to kill with song, that if someone heard a complete song they would soon die. When it is clear the keep is going to be overrun and horrible things happen to the residents, mother takes a wound, her daughter comes to her, mother wants to hear her sing for the first time (ushering her to the other side). When the attackers have breached the keep, Ellie begins singing a lullaby before she slits her own throat. Now, she fulfills her Banshee blood by roaming these lands, humming her lullaby as death approaches and keening when death is imminent. Don't stat her out for combat. She is something beyond blades and spells. There is no setting her to rest. This is who she is and was meant to be. Instead, the party's violence may attract the presence of the Banshee spirit, who hums or gently sings portions of her creepy lullaby (and I'd have an actual song ready to go, just take any number of Nursery Rhyme lullabies you can find online and change the words to fit a darker campaign).
B) Evil Banshee Dragonlance approach: Banshees in Dragonlance were elven women who committed horrible crimes and were condemned along with Lord Soth to eternal damnation as undead. The elven women would have to recount every night the fall from grace of Lord Soth and their role in it, aiming to cause him as much suffering as they can to lessen their horror of being trapped with him. It is a divine curse and cannot be undone so easily. This angle makes the Banshee a malevolent spirit. Perhaps instead of suicide, she betrayed her people and used the keep's attackers to carry out long-desired revenge on others. As they suffered, she reveled. As their children suffered, she gloated. As the attackers turned on her, the traitor, and killed her in the most unusual and horrific way, she cursed them one and all to join her. And perhaps soon after, all who heard her were killed (ambush, accident, etc.) Now, she sings like Soth's banshees to them, reminding them of their weakness, their monstrous nature, tied to them in an eternal knot. Putting it all to rest involves entering the macabre nightmare they dance each night, becoming a part of the original attack on the keep by taking on the roles of the cursed attackers, and reliving that moment over and over until, if ever, the party can figure a way to change events before their bodies waste away.[sblock]It's not about changing the past. This is a role-play scenario where the party members should be given scripts to play out of the attackers, written to focus on their rage and anger over the injustice of being trapped forever by the elf's curse. They can't change what happened, and that may be their first instinct. Each time as they approach that moment where she is going to curse them, they hate her for it because they know what she's done. The solution may be that they can't change what happened, but they can change the perception of the trapped spirits. Instead of hating her for cursing them, they could understand her. Not forgive her, not approve, but simply understand that she is bound by hate, and these monstrous attackers need not be bound by that same hate. They don't have to hate the defenders, the elf, the injustice of being trapped forever. They have to let it go. Once they're gone, she's got nothing to tie her rage to and she's gone to whatever special place awaits evil spirits. Anyhoo, there wouldn't be skill checks and you'd need some pretty solid roleplayers for this.[/sblock]
C) She's a Clue, not a Puzzle: You suggest it might be useful to tie her spirit into the hideout. This could be tied into either above if there was some connection, perhaps she visited the secret level for some reason, and the picture of her as a baby is in there, or she stashed bloody trinkets from her revenge victims before she was tortured by the attackers, etc. The mythology spirit might wander into a wall from time to time, suggesting another level, or the vengeful spirit might re-enact her death by stashing things, then returning only to be turned on by her former allies.
Ok, admittedly dark stuff, but as already posted, Halloween is around the corner and I'm already playing Curse of Strahd. This type of dark gothic stuff has been our bread and butter lately.
