SQLAgentOperatorRole User Unable to Edit Jobs in SQL Server

To make this happen, you need to give the computer domain account on which you have SQL Server installed rights to write to the share [Folder] on [ComputerName].

Say you have a computer SRV-SQLSERVER, and SQL services you run with NT Service*, but in some situation you can't create a domain account for them. But you need to store backups on other domain server \SRV-BACKUP.

To have this working, create an share on \\SRV-BACKUP\Folder and give write permission for SQL box domain account DOMAIN\SRV-SQLSERVER$.

Some related info can be found here:

How to grant network access to LocalSystem account?

I would work on educating your security team about jobs...they are server/instance level objects, not database level objects, so db_owner seems severely limited.

Ola recommends sysadmin for the job owners:

Which permissions are needed for the SQL Server Maintenance Solution to work?

If you are using SQL Server Agent, the jobs run under the SQL Server Agent service account that is a member of the sysadmin server role. If you are using a proxy account, I recommend that the account be a member of the sysadmin server role.

If you are using another scheduler, I recommend that the scheduler run under an account that is a member of the sysadmin server role.

If you need to have users execute the stored procedures ad hoc against specific databases, these permissions are needed:

DatabaseBackup: sysadmin

DatabaseIntegrityCheck: EXECUTE on dbo.DatabaseIntegrityCheck, VIEW DEFINITION on dbo.CommandExecute, VIEW DEFINITION on dbo.CommandLog, VIEW SERVER STATE, db_owner on all target databases

IndexOptimize: EXECUTE on dbo.IndexOptimize, VIEW DEFINITION on dbo.CommandExecute, VIEW DEFINITION on dbo.CommandLog, VIEW SERVER STATE, db_owner on all target databases

Regarding the comment about the msdb filling up if you run against a table, when you install his jobs using his big script MaintenanceSolution.sql he installs a CommandLog Cleanup job that will clear out the tables used to log his job steps.