I'm still a little foggy on this. Vince told the woman his wife found out and they needed to act quickly, but he also has said (to her and elsewhere) that he and Linda are married on paper only, they havent lived together in years, etc. So her simply finding out he was sleeping with this woman shouldnt have been an issue.
As for the why he needed her to do it so "quick" part this is where my financial reporting and reporting background in public markets could help me make a pretty strong educated guess. It was the way he hid things from others.
From the lawsuit
"On or around January 26, 2022, McMahon articulated an even more pressing need to get the NDA signed immediately, informing Ms. Grant that he was under a tight deadline to report pending or threatened legal actions to the WWE Board of Directors – specifically the Audit Committee"
Each year end, reporting teams / auditors send out letters to internal legal counsel and sometimes officers, asking them to disclose any open legal matters for which the conditions for that lawsuit existed before "x" date. In this case, it would have likely been December 31, 2021, assuming that is the WWE year end.
If Vince doesn't get this NDA signed before that deadline, either himself or his lawyer have to disclose the matter to the audit committee, the board, the auditors because it does involve the WWE and its an "open" matter... it goes in as a liability and expense on the WWE external financial statements, with note disclosure since its material and there has to be some public disclosure for it. Obviously Vince wants to keep things secret.
As an aside. Vince was always very careful in all his NDA's. They would always be signed by himself personally, and never anybody from the WWE, or his role as officer. But they would always be worded to clear the "WWE" from liability. And he paid for them personally In this way, nobody from the WWE (except his lawyer) knew about them so they were hidden from public disclosure. The finance team didn't know they existed, and since they never saw a payment made it was easy to hide from them, since they are at a distance.
This last part is why the WWE got nabbed by the SEC. The SEC said it doesn't matter if Vince paid for them personally, or if the WWE never signed them. These lawsuits were due to Vince's actions as an employee/officer and they reduced the exposure to the WWE -- hence the payments needed to be recorded in the WWE books.
Anyway, as a financial statement preparer, this case fascinates from that regard. There was very little they could to get things right on the statements, as Vince outright lied to them and was also careful where payments came from. It opened my eyes as to what could I have done in a similar situation.