I seem to have found a solution that worked for me. Like many others here, I too had greyed out podcasts that would not go away through normal syncing. I tried all the solutions recommended here, short of a full restore, and found that the podcasts remained only in my iPhone. As far as downloading them again for deletion purposes goes; my podcast episodes were only published for a limited time and thus were no longer available. Removing the entire podcast and unsubscribing in iTunes proved fruitless as the offending files would still remain in the iPhone after syncing.
I found my solution in the most obvious of places. Knowing that the "corrupted" files occurred upon deleting the individual podcast episodes directly from my iPhone and verifying there was no trace of them reflected in iTunes; I deduced that the issue at hand remained in the memory of the iPhone itself. Again, I had already worked all of the recommendations listed here short of a full restore and was looking for something less drastic. I went to the following location on my iPhone: Settings/Usage/-under the 'Storage' heading follow - Music/- under the 'Podcast' heading I found the offending podcast and swiped across to bring up the Delete button.
Once removed, I returned to the home screen and synced my iPhone as normal (via Wi-Fi if you find this detail pertinent). Upon completion the offending podcast was restored minus the grey "corrupted" file traces. Since this process only removed the specified podcast and its corresponding episode files, the restoring sync time was nominal.
I hope this may assist someone else in their solutions.
