On separate occasions, her name has been spoken in jest by Bert when Ernie asks if it was really him knocking at the door ("No, it was my Aunt Matilda -- of course it was me!"), had her birthday mistaken by Bert when trying to guess Ernie's surprise, and had her gift opened by Ernie.
In the latter case, Ernie finds a present in the apartment, and tries to guess what Bert is giving him. Ernie guesses that the present might be a football, a cake, or a reading lamp. When he's told that his guesses are wrong, Ernie excitedly unwraps the box. The present turns out to be a pink pillbox hat, with flowers and a veil, which Ernie commandeers. When Bert tries to explain that the hat was intended for Aunt Matilda, Ernie expresses surprise that he bought them both the same gift.
Coincidentally, Bert's pet pigeon Bernice also has an Aunt Matilda who resides in Brooklyn, as revealed in a 2004 sketch. Grover also mentions having an Aunt Matilda in another sketch; it is possible she is one and the same as his Aunt Mathilda.