In October 2002, Paltrow's father, Bruce, a film director and producer, died after a long battle with throat cancer. He was 58.
In her 2016 cookbook, My Father's Daughter, the Oscar winner opened up about the close bond she shared with her dad.
“I always feel closest to my father, who was the love of my life until his death in 2002, when I'm in the kitchen,” she noted in the book's introduction. "I can still hear him over my shoulder, heckling me, telling me to be careful with my knife, moaning with pleasure over a bite of something in only the way a Jew from Long Island can.”
Prior to posting a pic of the napkin message, Paltrow posted a photo to Instagram of her mother, Blythe Danner, at a climate march. "#blythedanner, always inspiring me with her conviction and her commitment to the environment," she captioned the photo.