In that particular scene, Connie is caught by Frank leaving a local bar where she just had a beer. She's plays a cleaning woman who works for Frank's awful brother (Arthur Kennedy), a bigwig in town and its biggest hypocrite who also employs her daughter (Nancy Gates) - and Connie is worried that her boozy afternoon indiscretion at Smitty's could cost both of them their jobs.
And Connie was also Gladys Glover's landlady in George Cukor's "It Should Happen to You" (1954), Gladys of course being Judy Holliday.
And throughout her career, Connie managed to look the same, ageless.
She was born in Brooklyn (where else?) in 1901, appeared on stage in France, England and New York and often played Irish (although she was actually cast as Señora Martinez in 1942's "Apache Trail," mother of Donna Reed's Rosalia). Chances are, if you were alive during the 1950s, had a TV or went to the movies, you saw her all the time. Like a family member or friendly neighbor, she was always around. Connie died in '85 at age 84.