How do I remove the 0.00 from the blank lines on my invoices

It's great to see you here in the Community, GT.

QuickBooks automatically eliminates blank lines when creating an invoice in the new experience. If you enter a character to preserve a line, a 0.00 will always show under the Amount column.

However, you can print invoices with blank lines using the old experience. Just ensure that you leave empty lines between your products/services. For your reference, see the screenshot below. 

Then, print your invoice right away. If you save it before printing, QuickBooks will remove the blank lines between your items. 

Learn more on how to tailor your sales forms to your needs by checking out this article: Customize invoices, estimates, and sales receipts in QuickBooks Online.

For future use, here's an article on documenting payments in QBO: Record invoice payments in QuickBooks Online.

Keep in touch if you have additional concerns about creating and managing invoices. I'm just one post away to help you out. Have a good day.