Ms Grisham, who served as White House press secretary and chief of staff for First Lady Melania Trump during the Trump administration, told CNN that the then-president had “lots of” closed door meetings which were left off his public calendar.
By having the meetings off the books, “anything that was written down could probably be thrown in the trash”, she said.
Ms Grisham, who has released a controversial tell-all book about her time with the Trumps, spoke out as the former president continues to try to block the release of National Archives related to the January 6 riot at the US Capitol.
The January 6 House Select Committee has requested the records as part of its investigation into the violent insurrection by Mr Trump’s supporters which left five people dead.
But, according to Ms Grisham, many discussions didn’t even make it into the records.
“Lots of meetings take place in the residence where I’m hoping they are looking at call logs but I have a feeling even that sometimes things weren’t even put into call logs,” she said.
Ms Grisham said the purpose of this was two-fold.
“A lot of meetings took place because the president at the time was so paranoid of leaks that a lot of meetings took place in the residence,” she said.
“Number one so that he could keep track of who was in there and that if it leaked out he could try to figure that out.
“But number two so that it was very much kept off the books and documents and anything that was written down could probably be thrown in the trash where people can’t come and retrieve them to put into the archives.”
She added: “So that happened quite a bit and I’m sure the Select Committee is aware of that and is looking into that.”
Ms Grisham claimed that former White House Chief of Staff Mark Meadows was involved in planning some of these meetings.
“Mark Meadows was one towards the end who was definitely helping to plan those meetings so I think Mark Meadows should be spoken to, I think that he will stall,” she said.
Mr Meadows failed to appear before the House Select Committee for a deposition on Friday morning in a move that now leaves him at risk of being criminally charged with contempt of Congress.
The former top White House aide had received a subpoena from committee chairperson Mississippi Rep Bennie Thompson to give evidence before the committee and hand over documents relating to the Capitol riot.
His compliance with the subpoena had been extended while he tried to negotiate the terms of his compliance with the committee.
But, on Thursday he was then ordered to appear the following morning.
Thompson and the committee’s ranking member Rep Liz Cheney confirmed that Mr Meadows was a no-show and said they were considering pursuing contempt charges.
His failure to show came the same day that Steve Bannon was indicted by the Department of Justice (DOJ) for contempt of Congress after he also refused to comply with the committee’s subpoenas.
Mr Bannon, who worked as an adviser to Mr Trump, was referred to the DOJN after a House vote last month.
However, the committee was dealt a blow on Friday after a federal appeals court temporarily blocked the National Archives from handing over records to the committee.
A federal judge had ruled on Tuesday that the records must be released by a deadline of Friday.
But the DC Circuit Court of Appeals issued a temporary injunction while Mr Trump continues to appeal against their release.
Mr Trump’s legal team has been given a date of 30 November for oral arguments for its appeal.
The former president has claimed that executive privilege means the records should not be released.
President Joe Biden has disagreed because Mr Trump is no longer president and so is no longer protected by executive privilege.
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