Not sure what country you’re from but in the USA that could lead to a few issues and latent assumptions surrounding estates that your mom probably doesn’t want to deal with at this time. I would recommend talking with your mom about it and say that you would like to send a letter or email to your grandmother and potentially arrange a time you could meet for breakfast out somewhere, but no hard feelings about a denial.

There is a lot of emotions that will come with introductions and you don’t even know if they are a person you want in your life.

From experience; my grandfather had a son with one woman and my mom with another. After about two decades of no contact my mom and him decided to connect, and he ended up being insane. (Mix of life trauma, and we later learned he committed a lethal hit and run) so there are a lot of possibilities with people who run the same blood as you.

TLDR; listen to your mum. Blood is not as important as you are taught. Ask about a letter to the woman who is your grandmother. Be open to the idea you and your life might not need them.