The British actress, 29, recounted the awkward situation on "Live With Kelly", noting that she was the one who urged them to watch in the first place, reported Us magazine.
According to Clarke, her parents had mentioned that her character, Daenerys Targaryen, did not seem to have much of a story line this season.
"Darling, you're not doing much," she recalled her father saying.
In response, Clarke urged her parents to watch the May 15 episode, to the point of actually joining them on the couch.