No, iframe is not a good desicion. The best option is creating a custom api. WordPress has a REST API with the ability to add custom endpoints:
https://developer.wordpress.org/rest-api/extending-the-rest-api/adding-custom-endpoints/
If you’re familiar enoigh with coding, you can create a custom api that shows the message that you want and in the client site, write a code for the dashboard widget to get the code.