DeLay, the former Republican House Majority Leader, dropped out of the show due to stress fractures in both of his feet. He promised to return and perform the Texas two-step in the season finale, however.
"I didn't want to go through another week like I had last week," DeLay told People magazine. "You have to practice."
"It's not worth the risk. He proved to everyone he could do it," added DeLay's professional dance partner, Cheryl Burke. "People are really behind this man. They love him. He earned some Democrat votes, as well."
Mazar, who has a recurring role on TV's "Entourage," described being booted off the show as a bittersweet experience.
"It's sweet because I don't have to kill my body another week, but bitter because I loved the experience," she told People. "I wish I had another chance to show that maybe I could leave my nerves at home and not bring them to the dance floor."
Mazar's professional dance partner was Maksim Chmerkovskiy.
Celebrity Families of 2014 [PHOTOS]