First to change the columns headers, you will either need to rename the columns being used OR you can edit the column definitions to Display a more user friendly column header name.
To show different columns
I can’t tell from the screen shot what data is being displayed in the Inline Table but it will have its own view listed in the system generated views. You can see these system views by scrolling to the bottom of the Views list in the UX tab and clicking this link to expand the view list:
To find the proper Inline view, find the data table in the views list that the Inline view is based on. Then look for a view with “_Inline” tacked on the end of the name.
You can edit this view just like a normal table to select which columns you want to appear and in what order
For example, I have an Inline table that uses data from the table named Materials. If I scroll to the views related to this table, I find one named Materials_Inline.
If you are still having trouble finding the correct view, re-post and I can walk you through it in more detail.