Hi there _G_
It's important that all your transactions are entered correctly for your books to be well balanced. QuickBooks Online is a great tool able to help you create and print cheques so you can pay your suppliers for their services. I can provide some information about cheques and taxes.
Within QuickBooks Online, when creating a cheque with a stub, the line item breakdown is shown on the stub, as well as the tax summary for the transaction. There isn't an option to remove the tax from the stub itself if you chose the cheque type as one with a stub. I can see that this would be a feature that you'd like to see to further customize the printing of your cheques. I recommend submitting feedback in the system by clicking on the Gear Icon, then Feedback. The comments made in that section are taken into consideration when designing new features for QuickBooks Online.
If you have any other questions, feel free to reach out here.