Blizzard has pushed an update to the Battle.net client, allowing players to disable the Last Played bar!
Battle.net Client Patch 2.22.0 Notes
Here are the patch notes for the recent Battle.net patch which allows people to disable the Last Played bar.
The Last Played bar was recently added for all players with no way to turn it off which frustrated players. This can now be disabled in the options by going to Settings > App > Show Last Played bar.