I would look at this very differently.
I am guessing that you store your data in a database. You have a Winforms app with a DataGrid that is a view of data in your database. This view allows you to also allow CRUD (Create/Add, Read, Update/make changes, and Delete). This should be it's sole purpose.
You have the need to do operations on your data that is not user tasks. One of these tasks is to check your database to see if a condition, or multiple conditions, has occurred. If so, then you need to notify the user, a customer, or some other stakeholder. This notification could be in the form of a popup window, a control on a form in the app, an email notification, etc.
Notice, as I describe each function of your app, it is showing how the design of the app should be done. In this case, of your notification, it is not part of the data entry (DataGrid). It is saying that it is a separate process. So, you should be using a Background Task, separate to the DataGrid, that periodically looks at the database.
You can read more about Background Tasks for Dot Net Framework here:
How to: Run an Operation in the Background - Windows Forms .NET Framework | Microsoft Learn[
^] or if you're using Dot Net core:
Create Windows Service using BackgroundService - .NET | Microsoft Learn[
^]
Hope this helps. 😊