Hi mate,
You mentioend that you recently started up. Did you inform the customer of this or that you were not a tiler by trade?
Rather than walk away or pay for someone else to do the job, I think that it is reasonable to alow someone to try and correct there work if anything should ever go wrong (unless doing so would make matters worse)
You could perhaps tell the customer that you will regrout or whatever you feel would rectify the problem and would not consider getting in someone else unless you had at least had the chance to correct the work yourself.
A tip is to inform the customer that you are new to the trade, et them know that you may be a bit slower than ana experienced tiler. You should reassure them that you can do the work to a good standard(if this is true) and even offer your services at a cost lower than experienced tilers untill you become more knowledgable and experienced.
AN ABSOLUATE MUST! = Do your research before starting any job, read around the forum and ask questions if unsure. You should have all angles covered sub floor prep, correct materials etc, etc, etc.
This bad experience is down to lack of knowledge and experience in the trade and I am sure you will learn from this. I have been on a few job were I have underestimated the scale of the work involved and it is depressing when you miscalculate or overlook what seem to be minor details. The best thing to do is 'bite the bullet' get on with it and learn from your experiences.
good luck with the customer mate, dont let it get you down, instead use this to motivate yourself and learn more about the trade to better yourself and be the best you can be.
kris