Dudek plays Danielle, who is unaware that her sister Annie (Piper Perabo) is working for the CIA.
Speaking to the New York Post, Dudek admitted that she did not know how big her character would be when she signed up for the show.
"It was an unknown thing when we started the series - what my role would be," she said. "Because I don't work at the CIA, how central can I be to what the meat of this show really is? I didn't know what that was going to be or how it could happen, so it's nice they've found a way to let Danielle infiltrate Annie's world."
Dudek added that she likes playing one of the "normal" characters on the show, saying: "To some extent, it's quite fantastical. Here's this extremely good-looking agent [Annie], travelling the world, having thrilling car chases with equally good-looking people and leading this exciting life.
"So it's nice to see this person go home to her sister, who has this normal family where the biggest drama is what will be for dinner. I like that our extreme action has this emotional counterpoint."
Covert Affairs continues tonight at 10/9c on USA.