Change SQL backup location
Editing the data in that table is not the correct way to make this change, as it is a system table. In fact, I don't think it is even possible, although some system tables outside of master can be updated.

If you want to do this via script, instead of manually editing your backup jobs, try this:

SELECT 'EXEC msdb..sp_update_jobstep @job_name = ''' + j.[name] + ''', @command = ''' + REPLACE(js.[command], '\\OldBackup\Share', '\\NewBackup\Share') + ''';'
FROM msdb..sysjobsteps js
INNER JOIN msdb..sysjobs j ON j.job_id = js.job_id
WHERE j.[name] = 'Backup Job Name'


This will dynamically generate a sp_update_jobstep command and replace the old backup share info with the new backup share info. Copy the generated results into a new query window, validate the job that's being updated is correct and the command looks correct, then you can execute.

Obviously, you should test this first and don't just execute it a production system.

More info:
sp_update_jobstep