Story highlights In a 2005 tape, Trump can be heard making crass comments aimed at Zucker

"For my family, I think, it probably hurts more than for me," Zucker told CNN's Anderson Cooper

(CNN) Arianne Zucker, the actress who was the subject of lewd remarks made by Donald Trump during a 2005 "Access Hollywood" shoot, said Friday that the tape's release has caused pain for her family.

"Of course, when people say things behind your back, they are hurtful, but we find a way to stand up and be strong," Zucker told CNN's Anderson Cooper. She added, "For my family, I think, it probably hurts more than for me."

In the tape, which was surfaced by The Washington Post earlier this month, Trump can be heard making crass comments aimed at Zucker as he prepared to meet her. At the time, Trump was talking with "Access Hollywood" host Billy Bush on a bus outside of the soap opera "Days of Our Lives," and the pair noticed Zucker, who was waiting to escort them onto the set.

The two then began making lewd comments about her.

Trump has apologized for the language he used in the hot-mic moment, calling it "locker room banter." But the clip -- and subsequent allegations of sexual assault this week by several women -- have roiled Trump's campaign. Trump has vehemently denied the assault allegations.