Vista Equity Partners — the giant buyout fund headed by billionaire Robert F. Smith — is hitting back at accusations of self-dealing by an ex-director at one of its software companies.

Earlier this month, Vista-owned Solera Holdings got sued by Kurt Lauk, a former board member at the software firm who claimed that Vista had pressed the company to buy some of its tanked investments at inflated prices.

Last week, the suit was tossed by a Delaware judge who cited concerns about his jurisdiction over the case, inviting Lauk’s lawyers to refile their case by Oct. 2.

The bombshell allegations have threatened to tarnish Smith’s reputation. Earlier this year, Smith made headlines nationwide when he surprised the graduating class of Morehouse College by telling them at their commencement he would pay off all their student-related debts — a promise he made good on last week by shelling out $34 million.

In a response filed Friday, Vista’s lawyers shot back on behalf of Solera with allegations that Lauk was a “crony” of the company’s ex-CEO Tony Aquila, who got fired in May over allegations of “aggressive and abusive” behavior.

In addition to lobbying for Aquila to get a $10 million bonus despite failing to meet performance targets, Solera claimed that Lauk “attempted to quash an internal investigation after a complaint (concerning a female employee) was made accusing Aquila of behavior in violation of Solera’s anti-harassment policies.”

Solera’s Friday filing claimed Aquila made “brash, vulgar, and belittling comments to colleagues resulted in … significant personnel turnover, including in the executive ranks.”

A lawyer for Aquila, who sued Solera on Sept. 4 over $100 million in stock options and compensation he claims he was wrongfully denied, has denied the allegations of harassment and abuse.

A Delaware judge last week threw Aquila’s suit into arbitration after Solera said it had enough funds to pay him if an arbitrator ruled in his favor.

In a Monday letter obtained by The Post, Vista’s lawyers pressed Lauk to drop his accusations. Echoing the allegations of their Friday court filing, they blasted Lauk’s claim that he tried to blow the whistle even as Vista had quashed Aquila’s promising idea to buy a software company called Lytx, while pressuring the company to overpay in a proposed acquisition of Omnitracs, a struggling firm owned by Vista.

“Lauk attended the board meetings at which Lytx and Omnitracs were discussed and had every chance to voice his concerns at that time. He did not do so,” Vista’s lawyers said in the Monday letter.

Vista likewise noted that it controlled Solera at the time and could have forced its agenda, but didn’t.

“It was not until more than a year after Solera evaluated these potential acquisitions that Mr. Lauk sent the letter to the board,” Vista’s lawyers added.

Lauk’s lawyer Sanford Michelman denied the allegations in both Vista’s Friday response and Monday letter.

“Vista’s self-serving statements are not a vindication of its inappropriate conduct that is rightfully alleged by Mr. Lauk in his lawsuits,” Michelman said.

“If Vista truly wanted to vindicate itself, it should open up its books and records,” he added. “I doubt that will happen without a court order compelling it to do so. That fact alone is telling.”