Which version of Finale are you using?
In Finale 2009 you can delete a measure this way:
Double-click the measure.
The measure becomes highlighted, and the highlighting goes about 1/2 "staff height" above and below the measure.
Hit the Delete key.
Finale 2012c, 2014d and 2014.5, Mac OS X 10.9.5, Dolet 6.6 for Finale, Finale user since 1996