The word must have been pissou.

Pissou is a colloquial word for a “wee”, a “tinkle”, mostly used with children. (From the French pisse → pee).
But it is also used to designate the genital parts, male and female (wiktionnaire). Not very commonly used that way though in France nowadays (I don’t know about Québec).

In this sentence it is used in a book about child’s psychiatry in a way of talking that addresses children:

.. se toucher le « pissou », cela le fait grandir jusque par terre, et après on ne peut plus marcher (Jean-Louis Lang – 1978)

For fun (only) L’association pour la réhabilitation du mot “Pissou”.

How your grandmother turned it into “pit-tow” is hard to say but it sounds possible to me. Both /t/ and /s/ are voiceless alveolar consonants in French and on top of that pronounced by someone who did not master all the French sounds.

As an aside, note that un pissou in Québec French is also colloquial for a coward. Some say that it derives from the English “peasoup”, but and others from the fact that a child who urinates is bed used to be called un pissou (or pisseux according to regions).

It’s a strange use, as I think she must had used the word pitou (pit-tow)

Which could be based off as pitounne, that can be used as a word to describe a beautiful women in Quebecois, but not her intimate part.

A note for pitou, if you check a dictionnary it would refer a synonym of the word dog, but in a slang use, in example a bar in Quebec, You could hear that word from a women to a men; ´Calme toi pitou’; there the meaning is a to calm down, as a pitou is seen like a dog that try to swing any other dog around.

It’s maybe a wrong word to describe her intimate part, but as you can see the word pitou got a strong indirect meaning

A word near pitou is minou, which could be used in Quebecois to pinpoint a vulva; ex; ‘Elle ma montree son minou..’.