She is first mentioned in The Kiss when Jay tells everyone that his father had kissed him one time in Jay's entire life and that was when one time he came up behind Jay, kissed him on the back of the head and said "Goodnight, Becky.", thinking that Jay was Becky.
Becky has a son named Brian and it is his wedding which Jay, DeDe, Claire and Mitchell attends in the episode Sarge & Pea.
In "The Escape", Becky makes her first appearance. She is in a nursing home, recovering from a stroke. It is revealed that she is a mean woman and such a monster and she and Jay have their differences. Becky and Jay hadn't spoken in 9 years and she had met Gloria only once, at their wedding. When Claire and Mitchell were kids, they were very frightened of her. Claire brings along a tomato soup. Jay's father had also promised that his fishing cabin would go to Jay, but instead he gave it to Becky.
At the end, Becky reveals that her brain is fine and that the doctor who was tending to her is actually just a guy named Fred who was from next door, played a doctor on a soap opera once and he had kept the coat.