Can you uninstall the application? Or is it one of those pre-installed apps?
If it's preinstalled, you'll have to get root access to remove it completely, see here.
However, removing it can potentially cause a brick if you factory reset your phone.
EDIT: It looks like there are no easy ways to disable this app. You have two choices:
- Factory wipe. During setup process, do NOT enable the backup assistant.
- Do some trickery using this method mentioned in this post (quoted below). It does not require a Factory wipe.
1) Be sure to have all your contacts backed up to your Gmail account. Check
online before proceeding to step 2.
2) Log into your My Verizon account.
Go to the contacts tab, sort by list
view and select all contacts. Delete
the entire list. There's a deleted
contacts tab as well. Select that and
delete anything that's in there.
3) Go into your Incredible settings
tab, select applications, manage
applications. Do not sort or filter,
allow list to populate. Select Sync
Service, (icon resembles backup
assistant icon) select clear data.
4) Also in manage applications scroll
down to backup assistant, select clear
data. This should do it.
5) To verify backup assistant is now
disabled, select settings, accounts
and sync, then under manage accounts,
select backup assistant. You should be
looking at a license agreement screen.