The functionality you require is not possible due to the fact that the Data.svc service that populates the dynamic content backend grid is internal an therefore there is no way for you to extend the default source it binds to the control.
You are able to add filters to the grid as explained in this blog post
but there is no way to add permissions to a filter.
Ivan D. Dimitrov
Do you want to have your say in the Sitefinity development roadmap? Do you want to know when a feature you requested is added or when a bug fixed? Explore the Telerik Sitefinity CMS Ideas&Feedback Portal
and vote to affect the priority of the items