Sorry for facing this issue, it's my pleasure to help us.
Welcome to the Shopify community!
and Thanks for your Good question.
Please share your site URL,
So I will check and provide a solution here.
Can you please share some screenshot/image from where you want to remove shop now option?
@kldlaz You are talking about shop now text which display on below image? If yes then to check the setting on your shopify store you need to provide access to your store
@kldlaz Here is the official help from shopify to change menus on messager
Go to "Customize the Messenger menu" on above page
Here is the image for section on help page :