ShareGate Migrate allows you to choose the view to use to display items both at the source and at the destination. The view selector is set to Built-in by default, which is an artificial view used within ShareGate Migrate to return all items (since a view in SharePoint might have a filter that does not display all items).
Prerequisites
You are connected to your source and destination libraries through Copy content.
How-to
To switch from one view to another, click on the drop-down menu located at the top left of your content (the dropdown defaults to a Built-in view that displays everything in your list or library).
Your content will automatically be refreshed with the items corresponding to the view you have chosen.