Synched photos can neither be deleted nor edited, because they are not stored in the Photos Library. To be able to edit them you have to save a copy of the synced photo to Photos. try to duplicate the photo you want to edit. The copy will a photo that can be modified, like a photo taken with the camera.
If the synced photos on your iPhone are the only copies you are having left of the old photos, you may want to duplicate all of them to save them on your iPhone, because previously synced photos will be replaced by the new photos, if you ever want to sync the iPhone again with a computer.