Hey Tracy, The close page activity will execute in the browser a back-page action, just as you're used to on other websites. Normally in Mendix you start from the home page and start navigating from page to page. The navigating will create a history off all pages that are shown and when a close page activity is triggered it will go 1 step back in the history and remove the current step.
With deeplinking there isn't a history to go a step back.
Normally: Start with Homepage -> Show Overview Page -> Edit an item. In this history you can go back to Show Overview Page and the Edit an item page will be removed from the history.
Deeplink: Edit an item. There isn't a history to go a step back.
The best thing you can do is to make sure that the user will be directed to the specific page or his home page when he has been redirected to the page by a deeplink.
What happens if you replace the 'close page' button on your edit page with a microflow that uses the 'close page' activity and then does a 'show page' where the call is to the page with the data grid? I am curious to see if this would work for you. You could expose this microlfow to anonymous users and make this the 'close action' microflow.