Square's integration allows MassageBook to send over a raw amount to be paid. This is referred to as a "Custom Amount" and means that Square doesn't detect whether a transaction coming from MassageBook is a Product or a Service.
If additional taxes are being applied for your MassageBook transactions, open your Taxes Menu in Square, and deselect "Custom Amount" from each of your Taxes. Doing so will ensure that no tax is applied when MassageBook sends a raw amount to Square to be paid.
Here's how it works:
If you open your Square POS app, and select "Keypad", and enter in $1.00, that is considered a "Custom Amount". If you do this as a test, and see that tax is added to the transaction, you have a tax set up in Square that applies to "Custom Amount" transactions. Depending on what % taxes you have enabled in Square, it may look something like this screenshot below. In this screenshot there is a $1.00 sale, with .10 tax applied. However, the receipt stored in MassageBook does not show the .10 tax as it is a tax initiated in Square. This will be broken down and stored in your Square account only. For online purchases, if taxes are enabled in your Square desktop account and not just in your Square POS app, the taxes will be charged and shows in your MassageBook receipt as a tax when client purchase online through your booking page. 
Using the example above, opening up the Taxes menu in the Square POS app reveals that there is one tax set up that is applied to "Custom Amounts". This same tax is going to be applied any time a transaction is generated in MassageBook, since Square treats the data from MassageBook as custom amounts. See the screenshot below:
After deselecting "Custom Amount" in the screenshot above, only $1.00 is due: 
All transactions generated in MassageBook will not be subject to additional Square taxes.
What if I want to tax Products only?
Enable Taxes for Products in MassageBook and turn off Square taxes for Custom Amounts. Then, when you sell a Product via the MassageBook Cash Register, tax will be applied before the transaction is sent to Square. Since no "Custom Amount" taxes are enabled in Square, the correct amount will display in your Square app.
If your business taxes Services but not Products, set up a Service Tax in MassageBook, and turn off Square taxes for Custom Amounts.
What if I want to tax Services only?
Enable Taxes for Services in MassageBook and turn off Square taxes for Custom Amounts. Then, when you sell a Service via the MassageBook Cash Register or checkout an appointment, tax will be applied before the transaction is sent to Square. Since no "Custom Amount" taxes are enabled in Square, the correct amount will display in your Square app.