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, Gloria, Mitchell, Cam, Claire and Phil all go to visit Becky in her room where she is fast asleep with the "same mean old puss on her face." She then wakes up to find her relatives in her room. A doctor comes in and tells the family that the stroke may have scrambled some of Becky's memories. She doesn't remember Mitchell coming out as gay and asks Jay if that summer if she could borrow his fishing cabin (It was originally Jay's father's cabin and he had also promised that it would go to Jay, but instead he gave it to Becky, so it's actually hers). Claire sees a necklace which Becky says she got from the prince of Liechtenstein, but in actuality, it is Claire's necklace which Becky stole from Claire when Claire had lent it to Becky for Jay and Gloria's wedding and she never gave it back to Claire. Claire takes the soup to heat it up so maybe the smell would jog her memory.
At the end, Becky reveals that her brain is fine, that her memories didn't get messed up at all and that the doctor who was tending to her is actually just a guy named Fred who was a friend of hers from next door who played a doctor on a soap opera once and he had kept the coat. Claire and Mitchell come back in and then Claire attempts to fool Becky again to get the necklace back by saying that she got off the phone with the prince of Liechtenstein who said he's been having some financial troubles and that he's gonna need the necklace back to feed his people, but Becky stops her. Jay then reveals to Claire and Mitchell that there was nothing wrong with her memory and that she was messing with them. They are really furious and Claire demands Becky to give her necklace back, but Becky refuses to give it back until Claire fixes the dent she put on Becky's Bonneville car which is still on it and she keeps the necklace when Claire doesn't sound like she denies it. In the ending scene during the credits, Claire is in her car and Phil comes running really quickly. When he gets inside, it is revealed that he gave Becky a hug goodbye, used his sleight-of-hand and on the third try, got the necklace back, which makes Claire really happy. As they prepare to leave, Claire opens up her camera from behind the car to reveal Becky riding along on her electric scooter telling them to give her the necklace. But Phil and Claire escape once the latter pulls off really fast.