"But they have gone to one of our customers and demanded 15% of their bill be retained and sent to the ATO."
I suggest you speak with your legals about the process.
Firstly I would challenge the legal right of the ATO to commence, and then threaten to carry out this action.
Be specific and ask the ATO exactly under which law, which act and which section of the act is the law valid. And ask for a printed hard copy of the law to be posted to you. Ask exactly on which date was the law passed, on which date did the law receive mandate from the voting public, and exactly which day did that law receive royal assent. If the ATO is unwilling/unable to supply the documentation within 21 days refer to your legals for defence. I am learning there are a lot of "laws" that have been made up. They are unlawful, illegal, repugnant and not valid.
Remember always harassment and intimidation is considered unlawful and can easily be challenged.
Secondly I would be asking the ATO (in writing) what would be the repercussions to both yourself, your company, and your customer, should your customer be unable/unwilling to send the money to the ATO. Strongly emphasis the question is of a totally hypothetical nature only. Would the ATO then remove without notice the amount from your customer's bank account?
If it was me I would get nasty and provide notice to the ATO you are now withholding payment of exactly the same amount should the threat of garnishee continue and that you will continue to with hold the sum until such time the matter is dropped. (however I am not offering you advice, it is only what I would do because I am a grumpy nasty old man, for these exact reasons)
"Firstly how do they know my customers"
They follow the trail of money.
If you trade as a company your accountant has access to your invoices and bank account records when working on tax returns which the ATO can vet.
"and secondly what now do you think that customer thinks of my company"
Important point. Would be interesting to discuss privacy laws and damages to your good name and the good name of your company.
Maybe discuss with your customer if they are open to it.
All of this is pointing to one thing.
The country is broke and only continues to operate (for the short term) using smoke and mirrors and unlawful laws.