In an interview with USA Today, the five-time BAFTA winner marvelled that the BBC One series has proved popular in America.
"It's on a continuous loop," she jested. "They can't help it! It's in front of them."
The actress added: "I had a woman writing to tell us she was sending a quilt for the bed because that's not the kind of quilt we'd have. Very curious."
As Time Goes By chronicled the lives of two long-lost lovers for nine series, before wrapping up with a reunion special in 2005.
Despite a string of award-winning performances in both television and film productions, Dench revealed that she now tries to avoid reading criticism of her acting.
"I don't read them now. You get to know because people tell you, of course... You have a shrewd idea of how things went," she added.
Dench will next star with Michelle Williams and Kenneth Branagh in My Week With Marilyn, which is scheduled to be released in US cinemas later this year.