The "Pearl Harbor" beauty has been linked to the "Saturday Night Live" star, who is 20 years her junior, for the past couple of months, but she never expected their relationship to draw so much attention in the press, and admits it can be a little overwhelming.
"I've never been in this position before - never dated anybody who comes with their own bag of mischief," she tells The Los Angeles Times, appearing to refer to Pete's broken engagement to Ariana Grande and his suicide scare last year (2018).
"It's all quite shocking, and something to get used to."
Kate, who previously dated actor Michael Sheen and was married to director Len Wiseman for 12 years until 2016, indicates her romance with Pete is serious, because she wouldn't put herself through the public scrutiny for a fling.
"I think if you liked the person less, you would bow out of it," she muses. "If that were the main thrust of the relationship, there would be a problem. But it's not."
The only aspect of the heightened paparazzi attention Kate isn't a fan of is her loss of privacy.
"I'd rather not have people hiding outside my house," the 45-year-old says. "It's a little old-fashioned to have a woman's personal life (looked at like that). It's a little bit tired."
Kate's comments about her new relationship emerge days after she introduced Pete to her mother and stepfather over dinner in Los Angeles, and shortly after the funnyman addressed the apparent controversy over their age gap during a segment on "Saturday Night Live".
"Apparently, people have a crazy fascination with our age difference, but it doesn't really bother us," he shrugged.