No, I have not seen a way to delete this. It's simply used as a handy reference to get back to reports you were looking at. Could you share your use case on advantages behind deleting recently viewed reports?
The way things have been implemented, we have some reports that show up with the same name but using the wrong value (say, an evar instead of a prop, because the eng team named them the same). So, the report history can lead to the wrong report. Our user was trying to clear it so she could go back to the right report in the future.