Gertrude (possibly Gertrude Turner), is the sister of Pappy Turner or Grandma Turner, the aunt of Mr. Turner, and the paternal great-aunt of Timmy.
Aunt Gertrude is first referenced when Timmy wishes a more exciting video game in the episode "Power Mad!", an "underwater version" of her house is shown, and even an underwater version of her is presented as a lobster. She likes to pinch Timmy's cheeks.
Aunt Gertrude has only appeared as a crab monster in the series, as the boss of the eighth level in a challenging video game Timmy wished up. From her appearance and mannerism of speaking, she is likely elderly.
Aside from her one appearance in the submarine level of "Power Mad!", not much background is known about her. It should also be noted that Vicky also knows her because she recognizes Gertrude's house and the fact she is Timmy's aunt. Her existence (as Timmy's Great Aunt) was confirmed in the "77 Secrets of The Fairly OddParents Revealed!" on Timmy Turner's character card.
In her appearance in "Power Mad!", she is the boss of an underwater level in a challenging video game Timmy's fairies wished up for him. He flees from the crab version of Aunt Gertrude, who wants to "pinch his cheeks". Timmy manages to swim to a Wanda coin, who puts metal protectors on the sides of Timmy's face. When Gertrude tries to pinch him, she shatters and explodes, allowing Timmy to move onto the next level.