With the selection tool, select those measures and DELETE. Or, select the measures, right-click on a staff in that selection, and from the context menu, Delete Measure Stack. Or, select the measures, Edit menu > Delete Measure Stack.

To select a measure:

Selection Tool.

Double-click the measure.

When a measure is selected, you can extend the selection via Shift-click.

Edward Leavitt,

Perhaps a bit more clear, there are two types of 'delete' in Finale. If you select just one measure in your piece or several in a staff line, Finale simply deletes the contents of that or those measure(s). Not the measure(s) themselves. Simply click on any measure, press the delete key.

The other delete which does remove contents and the measure itself requires all the staves in a stack be selected. Top to bottom.

Double-click a measure to select the full measure stack, or Alt-click on WIndows.
Press the delete key, or choose Edit > Delete Measure Stack. This removes the selected measures from every staff.