I just used The Works toilet bowl cleaner as described above. Thanks for the tip--it worked!
I was not able to flush all the water out, so I poured half the bottle in and let it sit for 30 minutes--then brushed. The plummer who was here after we failed to clear the blockage with an auger said we would not be able to get rid of the scratches--he was WRONG! Thanks!
I did this too and a suggestion on the internet was to use an acid based cleaner to clean the scratches. I found a bottle of The Works toilet bowl cleaner amongst our cleaning supplies. The label said the active ingredient is hydrochloric acid. The price on the large bottle was $1.00 (not sure where it was bought but maybe a dollar store). I drained the toilet, and put a folded paper towel saturated with The Works cleaner on the scratched area and left it there for a couple minutes. Then I wiped it off and was quite pleasantly surprised that it worked perfectly and easily. Worth a try.
Barkeepers Friend or Pfaltzgraff Stoneware & Porcelain Cleaner. I use them on my dishes and sink, don't see why they wouldn't work on a toilet. You'd just have to drain the water from the bowl first. You can get both at Bed, Bath & Beyond.