The phrase "that regardless" is grammatically correct and can be used in written English.
Example: I told him that regardless of the outcome, I would always support him.
Jesse knew that, regardless of how angry he'd been with Walt.
It seems that regardless of how erratic his personal life is, his music remains consistent.
DR. TYSON -- I would submit to you that, regardless of what the I.A.U.
But he added that regardless which photograph Mr. Fairey used, the copyright issues remained unchanged.
He sounded so unwell that regardless of my own feelings, I was worried for him.
But others warned that, regardless of motivations, the site was dangerous.
They worry that regardless of whether such laws are enacted, the sentiment will spread.
She said that regardless of his crime Williams did not deserve to be physically attacked.
But analysts say that, regardless of who wins the election, Venezuela faces a grim economic reckoning.
"I will always think that, regardless of the outcome of the case".
Rachel Springall at Moneyfacts says that regardless of swap rates, savings rates are still going down.
