A more elegant solution would be to use some client-side script and to keep track of what elements of the job you've rendered on the client.
Think about your feed in Facebook. When you hover over a row, you're presented with different modification options (update, delete, hide, like, etc). Often, when you click on these, the UI changes to reflect your executed intent (something fades out, is redrawn, reworded or otherwise). This is client-side Ajax working with server-side code.
Consider what you users would like to do.
It's likely the users would want to leave items. So let them ;)
It's likely they may wish to delete an item. Render an 'x' image next to the line and, when clicked, call a web method that removes that ID from the table.
It's likely that they would want to update (or modify) a single element. Render a pencil beside the row and, when clicked, reveal an update interface of whatever sort is appropriate for your row of data, and send the update via Ajax to persist the changes.
There are some samples here
] using ASP.NET and jQuery/jQuery UI together to make things like this happen.
Another thing to consider...if you do leave it as is, why not add a CreateDate field and a 'deleted' field. This would allow you to keep a history of Job iterations/modifications and you wouldn't need to delete the records, just mark them as 'deleted=true' and not render them on the page.