Granny Grouch, Oscar's grandmother, appeared in Sesame Street's Season 2's premiere, Episode 0131. She knows that her grandchildren hate her big wet kisses, so she kisses them as often as she can. She returns to give her grandson another kiss in Episode 0161. Whether Granny Grouch is Oscar's maternal or paternal grandmother is unknown, as is her relationship to Grandpa Grouch.
Oscar's "Gram" appeared in Caroll Spinney's book How to Be a Grouch, but whether Gram and Granny are the same Grouch is grounds for debate. Oscar displays pictures of her in Episode 0669 and 0889, where in the latter Bob recalls their previous encounter.