The Infowars conspiracy theorist raged at the former president for recommending the Covid-19 vaccines.
Tom's wife of 59 years Linda Trenchard died in 2016 after being diagnosed with lung cancer.
The presenters were mortified to have fallen for the Bake Off host's story about the hit BBC police drama.
The BBC presenter remembered the researcher as being "hugely talented and such good company".
"To be fair, it's hot in our house," the Top Gear star joked on Twitter.
The presenter is about to go on a two-week break to spend time with her mother, who she hasn't seen in four months.
"I've got blood everywhere!"
"Wait... did that little fondant figure have a giant vagina on show?"
"This Sandy Hook stuff is killing us," the far-right Infowars editor said in a 2015 email.