The college admissions scandal that broke earlier this week has put the private equity firm TPG and one of its senior executives in a fight over whether he quit or was fired for cause.

On Thursday evening, TPG emailed a statement to CNBC's Leslie Picker that said William McGlashan, who had been the head of its growth buyout fund, had been "terminated for cause." He had been on administrative leave since Tuesday, after he was charged in the nationwide scheme that involved parents bribing college coaches and arranging for falsified standardized test scores to gain admission for their children to several elite universities.

"After reviewing the allegations of personal misconduct in the criminal complaint, we believe the behavior described to be inexcusable and antithetical to the values of our entire organization," TPG's statement said.

Dozens of people have been charged in the ongoing case.

But McGlashan is disputing the terms of his departure, saying he resigned. In an email to CNBC around the same time the firm sent its email, a spokesman for McGlashan said he has resigned from TPG's Rise Fund and TPG Thursday afternoon. "The progress we have made is too important for you to be distracted by the issues I am facing personally," said the text of a message from McGlashan to TPG board members that was forwarded in the spokesman's email.

TPG Growth has invested in startups like Airbnb and Uber. McGlashan, a Yale and Stanford Business School graduate, also started the Rise Fund, which is aimed at investments that promote social good. The Rise Fund first launched with the musician Bono and raised $2 billion in 2017. The second iteration of the fund recently had its first close of fundraising, which brought in another $1 billion, a person with knowledge of the matter said.

Given the McGlashan's implication in the college bribery scandal, TPG has told investors that they will have the opportunity to "reaffirm" their commitments to the second Rise Fund, or pull their investment if they so choose, a person said.

Prosecutors allege McGlashan paid $50,000 to the charitable arm of a college admissions counseling firm, which was going to correct his son's answers on a standardized test to boost the score. They also allege he arranged to fake an athletic profile of his son to help gain him admission to the University of Southern California.

CNBC's Leslie Picker contributed reporting.