You should continue upgrading, Netbackup 7.7.3 has been out of support for years.
You may be able to use filter option of the activity monitor. But I encourage you to learn how to live with the parent jobs, they are not going away.
As @Nicolai says, you should upgrade to a more recent version e.g 9.0.
I agree with @Nicolai about the parent/child view will not go away and has been definitely helpful in more than 1 way, but I was wondering if you were referring to the setting for Activity Monitor. Try toggling the View > Jobs in Hierarchical Manner, and see if it looks better.