Washington (CNN) Applying to college can make any high school senior feel like he or she is pleading a case before a judge and jury -- but one former Washington, DC, prep school student is trying to get her college woes heard by the Supreme Court .

Dayo Adetu and her parents, Titilayo and Nike Adetu, say that the private Sidwell Friends School -- the elite school attended by a who's who of Beltway families, including presidential daughters Sasha and Malia Obama and Chelsea Clinton as well as former Vice President Joe Biden's granddaughter Maisy -- breached a settlement with the family after it allegedly discriminated against Adetu, an African-American, in the grades she received while in high school and then in materials Sidwell submitted as she applied to colleges.

"Sidwell has long been perceived as a 'feeder-school' to Ivy League institutions and other top universities," the Adetus wrote in their appeal to the Supreme Court . Adetu, however, was not immediately accepted by any university.

The court is scheduled to consider whether to take up the case, along with scores of other petitions, at their private conference on Thursday.

The pressurized world of admissions to top-tier colleges has been a national focus recently following the sprawling scam that has implicated wealthy parents, Hollywood celebrities and college coaches, resulting in several guilty pleas

During her initial first round of applications -- when she applied to Princeton, Yale, Harvard, Columbia, Cornell, Penn, Duke, Johns Hopkins, CalTech, MIT, the University of Virginia, McGill and Spelman -- Adetu "was the only student in her graduating class of 126 students who did not receive unconditional acceptance from any educational institution to which she applied," according to the Supreme Court petition.

Adetu ultimately attended the University of Pennsylvania in 2015 after applying to colleges again, according to the complaint, and indicated on social media that she graduated last month.

The family is seeking review of a decision by the District of Columbia Court of Appeals in January that said the Adetus' claim was rightly rejected by a lower court because they had failed to show "any adverse action taken by Sidwell" and were only claiming emotional damages for an alleged breach of an earlier mediated settlement.

The petition is unlikely to be accepted by the Supreme Court, which takes only about 70 of the over 7,000 cases that it receives for consideration each year.

"It's more than a little unusual for the justices to take a case like this one that comes from the DC local courts and turns entirely on questions of DC local law," said Steve Vladeck, CNN Supreme Court analyst and professor at the University of Texas School of Law. "Although the court formally has the power to hear such disputes, and DC law is technically federal law, the justices tend to stay out of such DC-specific disputes."

Richard Baker, the Adetus' lawyer, told CNN that neither he nor his clients had a comment on the case. Brian Scotti, a lawyer for Sidwell, also had no comment. Sidwell, which opted not to submit a filing to the court in response to the Adetus' petition, did not respond to a request for comment.

Adetu was a student at Sidwell Friends from 2000 until her high school graduation in 2014, according to her family's initial complaint. A year earlier, when Adetu was a junior, she and her parents filed a claim with the DC Office of Human Rights, alleging discrimination and retaliation largely related to her math classes. The complaint specifically accused a math teacher of allegedly using "biased, improper scoring" to grade Adetu's tests and of having "steadfastly refused" to make accommodations for her athletic commitments while doing so for other students.

Sidwell and the Adetus then entered into a settlement agreement that dictated the school would pay the Adetus $50,000, recalculate certain grades and not retaliate against Adetu.

In the petition to the Supreme Court justices, the Adetus say that when Adetu applied to Ivy League and other competitive schools, she was not accepted unconditionally to any of them.

"Despite the fact that Sidwell touts a 100% college matriculation rate for its graduating high school seniors, Dayo did not receive unconditional acceptance to any of the thirteen (13) universities to which she applied and desired admission," the family wrote.

The Adetus filed a complaint in DC Superior Court alleging, among grievances, that Sidwell had breached the Office of Human Rights' settlement agreement. They contended Sidwell retaliated in materials included in her college applications, including test scores, rankings and recommendations.

The Superior Court ruled against the Adetus, finding that they "cited no evidence that Sidwell made negative comments about Dayo or otherwise interfered with her college admissions process, beyond plaintiffs' own speculation," and that there was no meaningful breach of the settlement.

The District of Columbia Court of Appeals affirmed that ruling in the decision now before the justices. Sidwell had described the Adetus' claim as "generalized gripes founded upon [the Adetus'] speculation" and argued that it was entitled to academic deference, the appeals court noted. The appeals court also ruled against the Adetus on the grounds that they "failed to make a sufficient showing that Sidwell engaged in 'adverse action' against Dayo or that objectively tangible harm resulted."