Sumner Redstone and his National Amusements (NAI) theater chain asked a Massachusetts court today to dismiss a plea by his granddaughter, Keryn, to investigate last week’s deal to settle lawsuits by former Viacom CEO Philippe Dauman.

In filings ahead of a hearing tomorrow, the 93-year-old mogul’s team says that Keryn’s lawyers have “strived mightily (but unsuccessfully) to initiate their own settlement discussions through every avenue imaginable.”

But the granddaughter doesn’t have standing to challenge the agreement, the lawyers say, because it involves Viacom — not the seven-member Redstone trust to which she’s a beneficiary. The trust will control Viacom and CBS when Sumner’s deemed unable to do so.

As part of the agreement, Dauman and Viacom director George Abrams dropped their effort to remain on the trust. Keryn can’t force them to “hold positions…that they have voluntarily resigned from and renounced any interest in holding,” the Redstone and NAI filing says.

Keryn asked Massachusetts Probate and Family Court Judge George Phelan to launch a “full inquiry” into the settlement, noting that Dauman resigned as Viacom’s CEO under conditions that entitle him to collect a $72 million payout provided for in his contract.

This “has all the hallmarks of an improper, self-interested transaction,” Keryn’s filing says. “At a minimum, it demands this Court’s close scrutiny and Plaintiffs’s forthright explanation under oath.”

But Redstone says that Dauman’s contract at Viacom was unrelated to the Massachusetts case about the family trust, and “there was no separate payment to Dauman in the Settlement Agreement, let alone any payment out of the Trust.”

Keryn’s lawyers say that the agreement “could have widespread and prejudicial implications” for her as well as “her enfeebled and preyed-upon grandfather. No one (other than Keryn) seems to have any interest in overseeing the fair, just and equitable administration of the Trust.”

Her team also says that negotiations to establish terms for a proposed September 1 deposition of Sumner have broken down over three issues.

Redstone’s team wants to limit questioning to 30 minutes. Since he grapples with a severe speech impediment, they want to pick someone who will interpret his comments. And they don’t want Keryn to attend.

The time limit illustrates how Redstone’s team has “conveniently run hot and cold when making representations about Sumner’s current condition,” Keryn’s filing says. The time restriction would seem to contradict their position that he’s alert enough to oversee a $40 billion media empire.

And Keryn “has a fundamental right to be present” at the deposition, today’s filing says. Keeping her out is “a misguided attempt…to exercise control over the proceeding and, hopefully, dictate its result.”

But Redstone and NAI say this is now a moot point. Dauman and Abrams’ suit “created the exigency warranting a highly expedited trial” about Sumner’s competence.

Now that they’ve withdrawn their case, the court should take “sufficient time” to consider the motion to dismiss Keryn’s suit, or set “a more reasonable schedule that will allow defendants to mount complete defenses in this case.”