The move by the Chief Justice was what is known as an 'administrative stay' - not really getting to the merits of the matter.
"This is a totally standard procedural move, nothing more," tweeted Steve Vladeck, a law professor at the University of Texas.
It's likely the broader issues could be considered at a regularly scheduled conference meeting on Friday, where the Justices consider whether to take up certain cases before the High Court.
The Supreme Court has several options - the Justices could allow the lower court ruling to stand, which ordered Mazar's to abide by the subpoena, and turn over the President's documents.
Or, the Justices could decide to hold a special set of arguments on the case.
President Trump's legal team has already asked the U.S. Supreme Court to intervene and block a similar subpoena from prosecutors in New York City, who are also seeking the President's financial records from Mazar.
The Supreme Court has not taken any action with respect to that New York case.
As for the matter involving the House Oversight Committee, lower courts have ruled against the President's bid to block a subpoena to his accounting firm as well.
In the New York case, the President's lawyers told the Supreme Court last week that Mr. Trump has 'absolute immunity' from any criminal investigation while in office.