Sprites were famous for their unrivaled ability at tracking mana, if she were to free the sprite it could easily track its owner to whom it was bound to by the enslavement seal. As for the seal itself, magical bindings such as those tend to be loose when used on beings said to be loved by mana such an fairies and sprites. Her seemingly powerful captors would have most likely tried to address that fact but it was impossible to cover them all safely, especially against low-level beings who would just die if they tried to forcefully bind them.
As for how the succubus planned to convince the sprite to risk its life to satisfy her greed, the rumors going around telling of the fate of sprites and fairies that got captured by powerful researchers and a bit of self-preservation should easily enough convince the sprite.
But it wasn't all greed that made the succubus plan all this. The mana-sealing collar around her neck was a bigger issue, it prevented her from refining any more mana and restricted the use of whatever mana she already had stored and it was slowly leaking out. If she were to use all the mana she had left to teleport out of here not only would she not be as far away from here as possible but she'd risk dying of mana deficiency. If the lock mechanism was magical she could easily break out of it, but it was also mechanical and the keys needs to be made of a specific material, which she has no idea what it is so she needed to steal a key from one of the guards. That was further made a problem since only the floor supervisors had the key and not only are they mid-level squires but they also rarely bother to show up unless there's a customer from what she's seen.
That made things easier for her since she wasn't sure the plan she cooked up would work on someone a full stage above her.
She needed a few formations for her plan, so after they had been given what was supposedly breakfast she started to discreetly construct them. She couldn't use her mana so she had to use the ambient ether instead. Formations that use ether were extremely rare so counters were rarely prepared and no matter how many times she scanned the area with her spiritual energy she couldn't find anything of that sort in her range.
She didn't have any formation ink so she defaulted to using her blood, since it was a part of her it would be easier to manipulate and imbue with magical properties. Untreated blood tends to slowly decay into dust after a couple of hours when used as formation ink.
She also had to make sure that the formations were efficient so that they would be harder to notice.
She used the hay strewn across the floor to construct the first formation array on the floor near the spot where she always sat. She etched the complementary formation on her inner left thigh.
For the second formation she rolled up the edge of her dress and constructed the formation on the inside. She straightened her dress after she was done and waited for the guards to serve lunch.
With lunch over with she moved on to the most troublesome formation. It was a 3D formation that would be good for the sprite should it decide to join her. She had to draw a bit of blood and imbue it with multiple effects across a number a layers without overloading the blood, and because it wasn't made with the proper base material it's effects would be significantly weaker.
That took a lot of time and she had to stop for a bit when the guards delivered supper. After supper she focused on finishing up the formation and ensuring that it is stable enough to last a couple of hours before it starts degrading.
With that done all she had to do was wait until she's sure that no more guards would arrive at the floor just as she was escaping. Once she was certain enough of that she used her spiritual energy to activate the formation on the floor.
It could be classified as mind control, it would subtly make someone ignore a certain thing which in this case would be the formation on the succubus' thigh and whomever else she decides to add. Since the formation was weak the succubus had to wait for a while to give it time to permeate throughout the entire floor and affect everyone.
Around half an hour later she stood up and walked towards the door taking care not to disturb the other succubi. Although the formation made them ignore her that was only true as long as she herself didn't bother them and she didn't do anything too drastic.
Reaching the door she carefully ripped off the edge of her dress that had the formation. Scanning the door with spiritual energy once more verifying that the lock mechanism is quite simple before she activated the formation. The formation started to pull in ether and release a dark brown mist which the succubus guided to the lock mechanism and the mist started corroding it.
With the lock mechanism corroded away she slowly opened the door and went through the moment the gap was big enough for her to pass through. Closing the door behind her, she went in the direction of the area where they kept those that have been bought.
Reaching the area she looked for the sprite of interest, it seems that they have kept the creatures according to who they belonged to. So she had to look for a sprite in the same cage with a mountain goblin, an incubus and possibly some other creatures. She was lucky to find the sprite dumbly laying on the floor near the outer wall, staring at the ceiling.
She reactivated the formation on the piece of cloth she corroded a big enough hole for her hand to pass through just off the ground. Putting in her hand she carefully positioned it near the sprite's head so she could cover its mouth.
Once ready she grabbed the sprite and pulled her hand back as quick as possible, before the sprite could even process what's happening the succubus was already hurrying to the closest edge of the floor.
Leaning against the wall she slided down the wall. After taking a couple of deep breaths to calm down she looked at the sprite in hand.
She was still covering its mouth, she had grabbed it by the head so that was given. Making sure that it could see her she signaled for it to be quiet. Once she saw that it had calmed down she concentrated on covering it with the effects of the formation. With that done with she had to sell it a bit of grand theft.