How to recover or reset "current backup password"
My little research here indicates that the current backup password is saved in the file /data/backup/pwhash (no plain-text). In some earlier Android versions removing that file followed by a reboot resulted in paving a way for setting up  new password since current password would default to blank then. But in Lollipop, you've to remove the file pwversion (in the same directory) as well.

Because the location is under /data/ you'd get "permission denied" message if you attempt to browse into /data/backup, be it from a file manager or from command-line, unless root access is provided. 

The only way (as it seems to me) to reset the password without root access is the factory reset.