From the API, there are several ways to recover filtered data.

To do this, use getTableValues, and add the filtered rows parameter, also called filterRowIds.

Use data from an existing view that has already been filtered: applyViewFilters
In filtered rows, enter the filter ID in the following ways:

{ "ApplyViewFilters": 12345}

It can be found in the XHR console under the name view_id:

Filter directly via the query: filterGroup
In filtered rows, enter the filter ID in the following ways:

In this example, I want to display all the rows in my table that have the text "hello" in the column with field_Id 320862.

Another example available in the documentation :

Filters list