Grandma Connolly

Grandma Connolly was Rita Connolly's mother, who lived with Rita and her husband, Eddie, and their son, Tommy in a home that she owned.

She was excited at the prospect of seeing the Queen's Coronation on television, and was present when the TV set was delivered from Magpie Electricals. However, it was playing up and the Wire appeared and stole her face. (TS: Tardisode 7)

Eddie Connolly, unbeknownst to his family, then reported Grandma to the police, who took her faceless body away and stored it in a lock-up with all the other locals who suffered a similar fate. When the Wire was defeated, Grandma's face returned and she went home. (DW: The Idiot's Lantern)

Behind the scenes
This character is never referred to as a "Connolly" in the dialogue of the episode, but it is how she was credited at the end of the episode. Also, her Character Options figure is clearly labeled "Grandma Connolly".  She is, however, positively identified as Rita Connolly's mother at least three times within the episode.  This implication of all available information, both in- and out-of-universe, is that Rita was a Connolly before marriage as well as after — something not outside the realm of possibility, given the fairly common British surname.