Hi @Liz_Radley, welcome to the Community Forum and thanks for reaching out!
You are right, the Asana and Google Calendar integration allows you to see your Asana tasks in Google Calendar but not the other way around. We have a very popular request in the forum about this topic: Real time, two ways Calendar integration. I recommend you to upvote and check all the information shared in the thread!
Let me know if you have any questions!