Hello Kimpossible,
Welcome to Mrs. Clean!
I've searched for information in the mfg'er of this product, but have come up empty. I do have a low cost/low labor item to try. If this does not work, please provide info from the product label and I can research further.
This may make you think twice about drinking "the real thing" but it's the high pH/acid that works to dissolve stains.
I'd let it sit on your stain for 8-12 hours (at least) given the fact you had let the ty-d-bowl toilet cleaner sit while you were on vacation, which is likely why the purple dye has stained the toilet bowl.
Cleaning the toilet with Coca Cola
Pour one or two cans of Coca-Cola (not diet) into the toilet bowl.
Let the soda sit for at least 2 hours.
Brush with toilet brush and flush.
Your stains should be gone.