This is not possible through settings in the datagrid.
However, this is possible by using an entity with a search string attribute on the page. Add the entity as parameter of the datasource microflow and use the attribute to filter your data.
Hope this helps!
The solution Pedro provides is a good one, another one that can be useful is using a persistent entity as a page parameter with an association from the entity that you want to show in your datagrid & an association to the session entity with delete behavior to make sure the object will be deleted after the session ends.
Before opening the page, retrieve or create an object from your new entity and occupy the first association with the objects you want to show in your datagrid, and the second with the current session.
The downside is that this affects your domain model and some data will temporary be stored in your database, but it will allow you to use the default datagrid options and avoid the introduction of inconsistent custom UI building blocks. This is also useful in cases where you are reusing the same set of objects.