Having worked with TB's, I would not recommend just leaving her tied, nor would I do any of the "tricks" usually done to cure a horse of this habit. And that includes hobbling too.
This breed will panic and even kill themselves in that panic.
They react differently to many things and this is one of them.
Broken legs, neck, spine are only 3 things that can happen in situation like this. These horses are only tied in stall for the most part, and outside that stall are held by groom while being worked with.
This is a PDF document that will help with transitioning a OTTB to a new life, and also even a TB new to being a pleasure horse.
This portion is from that document link. Does my horse know how to tie? The answer is yes, but it is important to understand that the method and place for tying a young Thoroughbred horse is different than a pleasure horse. The first, and usually the only place, these colts and fillies are tied is in the back of their stall, usually with a flexible rubber tie bar, where they will learn to stand while being groomed and tacked up. They are always held by a groom when standing out side of their stall for shoeing, bathing, etc. NO Why are Thoroughbred racehorses only tied in their stall? The primary reason is safety. Young Thoroughbreds are valuable and their owners have paid many thousands of dollars for them as racing prospects. Keeping them confined in side their stall while tied is the surest way of preventing them from breaking loose and having an accident. The second reason is that they must learn the routine of the racetrack. Keeping the young horse quiet and unexcited when tied is essential for both his and his handler’s safety. This should be learned before being taken out and is just laziness on the breedr/trainers part if not already done so Training tips for tying your Thoroughbred: Since your horse has probably NEVER been asked to stand tied outside of his stall in the midst of other activity, begin by doing what your horse is comfortable with. Tie him first in his stall where you can become familiar with each other in a safe environment . Never tie him outside and leave him when you have not trained him to stand quietly.
When your horse knows and trusts you it is time to make him familiar with standing tied outside of his stall for grooming, tacking, and bathing. Work with him to stand quietly with you for increasing amounts of time. Loop the lead rope looped through the tie ring or rail, and hold the rope in your hand to give and release. Gradually increase his comfort level so that he has less fear of confinement, and becomes accustomed to standing quietly outside. This should have been done with him as a yearling when preparing the horse for the sales. http://www.tranquilityfarmtbs.org/pdf/retraining.pdf
This is not always so - it just depends where the horse was raised or trained. At the places I've worked all were taught to stand tied up both inside and outside of their box. In the hosing bay and on the walker.
At the trainers they are often cross tied but are expected to be tied up both inside and outside their box.
Once off the track the majority of TB's in NZ become riding and competition horses and you see them all over the showgrounds tied to their horse floats and trucks. Its a myth that TB's can't be tied up. They are just horses with a different job.
The majority if my school horses were TB's and taught beginners to ride, they all stood tied up while waiting and this was expected of them from day one. I'd get lots of them too as the owner of the school had brothers who trained and the rejects would come straight to me for schooling and rehoming.
Only the odd few are nut jobs and that can be the same for any breed - I've known nutter ponies that can't be left tied up.
They pull back because at one time they did it, got away with it, maybe panicked a few times and then their owners declared they could not be tied up.
Some pull back with very careful thought and its not because they are panicked they do it because they can - ever had the horse that will stand quietly, then give the baler twine a quick snap back? Then stands quite happily untied or wanders off to quietly graze.
I've used the bum rope on any of the naughty ones I've had with great success - you do have to make sure that you chose a safe place for this initially where the horse can't slip over - but most once they feel the pressure behind them will stop pulling back and once the pressure has gone from the top of the head they stop trying to pull back.
One thing that needs to be done for any horse that pulls back is a visit by the chiro because at the time they pull back they put a lot of pressure on the Atlas and Axis at the poll and often twist their heads from side to side risking twisting the whole joint out of alignment.