I've run into similar requirements before, and the only sure solution I know of is to use a copy of your production database. You can mask/delete data on the copy and run backups from there. Yes it's ugly and a waste of resources, but to date I haven't found a solid alternative for this particular problem.
As for the copy method, you do have some options:
- Replication
- Scheduled DB copy
- Backup/restore from production
So while I admit this solution is pretty cringe-worthy, it can be automated and serve your purposes. If you can find productive uses for the database copy that don't require your deleted information (e.g. reports, testing, development) then this can actually be a less-than-terrible solution. It can be a nice security boon to have a slightly out-of-date version of your production database with sensitive data removed.