Can't delete folder of photos from my iPhone which was synced from iTunes. There's no trash icon.

You can't delete it directly on your iPhone, it can only be deleted by changing your photo sync selection on its Photos tab when connected to a computer's iTunes. You can delete all synced photos from your phone by selecting and syncing just an empty folder on the Photos tab. If you want some synced albums to remain on the phone then you will need to copy them onto your computer first so that you can include them in the photo sync.

If you don't have a copy of the photos anywhere on your computer and/or on a backup drive and you want to copy them off your phone first then there are apps for your phone such as Simple Transfer Pro which can copy them off via your wifi network - though as photos are 'optimised' when they are synced to a device, any that you copy back may not look the same as on the computer that they were synced from (e.g. colours might look different and the photo dimensions might also be different)