Justice Thomas can refuse to do anything with it, or can bring it before the other Justices for review.
Of all of the cases floating around in the legal system, THIS case is seen to be on very good legal standing.
From http://www.blogtext.org/naturalborncitizen
Barack Obama's official web site, Fight The Smears, admits he was a British Citizen at birth. At the very bottom of the section of his web site that shows an alleged official Certification Of Live Birth, the web site lists the following information and link thereto:
FactCheck.org Clarifies Barack’s Citizenship
“When Barack Obama Jr. was born on Aug. 4,1961, in Honolulu, Kenya was a British colony, still part of the United Kingdom’s dwindling empire. As a Kenyan native, Barack Obama Sr. was a British subject whose citizenship status was governed by The British Nationality Act of 1948. That same act governed the status of Obama Sr.‘s children.
Since Sen. Obama has neither renounced his U.S. citizenship nor sworn an oath of allegiance to Kenya, his Kenyan citizenship automatically expired on Aug. 4,1982.”
That is a direct admission Barack Obama was a British citizen "at birth".
Since Barack Obama's father was a Citizen of Kenya and therefore subject to the jurisdiction of the United Kingdom at the time of Senator Obama's birth, then Senator Obama was a British Citizen "at birth", just like the Framers of the Constitution, and therefore, even if he were to produce an original birth certificate proving he were born on US soil, he still wouldn't be eligible to be President.
The Framers of the Constitution, at the time of their birth, were also British Citizens and that's why the Framers declared that, while they were Citizens of the United States, they themselves were not "natural born Citizens". Hence their inclusion of the grandfather clause in Article 2, Section 1, Clause 5 of the Constitution:
No person except a natural born Citizen, or a Citizen of the United States, at the time of the Adoption of this Constitution shall be eligible to the Office of President;
That's it right there. (Emphasis added.)
The Framers wanted to make themselves eligible to be President, but they didn't want future generations to be Governed by a Commander In Chief who had split loyalty to another Country. The Framers were comfortable making an exception for themselves. They did, after all, create the Constitution. But they were not comfortable with the possibility of future generations of Presidents being born under the jurisdiction of Foreign Powers, especially Great Britain and its monarchy, who the Framers and Colonists fought so hard in the American Revolution to be free of.
The Framers declared themselves not eligible to be President as "natural born Citizens", so they wrote the grandfather clause in for the limited exception of allowing themselves to be eligible to the Presidency in the early formative years of our infant nation.
But nobody alive today can claim eligibility to be President under the grandfather clause since nobody alive today was a citizen of the US at the time the Constitution was adopted. The Framers distinguished between "natural born Citizens" and all other "Citizens". And that's why it's important to note the 14th Amendment only confers the title of "Citizen", not "natural born Citizen". The Framers were Citizens, but they weren't natural born Citizens. They put the stigma of not being natural born Citizens on themselves in the Constitution and they are the ones who wrote the Document.
Since the the Framers didn't consider themselves to have been "natural born Citizens" due to their having been subject to British jurisdiction at their birth, then Senator Obama, having also been subject to British jurisdiction at the time of his birth, also cannot be considered a "natural born Citizen" of the United States.