Hi partner,
Extended Amount is a field of Invoice Line, it shows the total amount due for the invoice product, based on the sum of the unit price, quantity, discounts, and tax.

Please note that Extended Amount represents the total amount of Invoice Line (Invoice product), not Invoice.
In addition, it is locked, we cannot modify it.
So does "extended amount" refer to Total Amount? because we can modify it in the head.

If so, it shows the total amount due, calculated as the sum of the products, discount, freight, and taxes for the invoice.
Its value is actually automatically generated based on Invoice products. Of course, you can also modify it manually on the head. After you change the Invoice product, it should be updated automatically.
The problem you are experiencing now is that Total Amount is no longer automatically updated, right?
If so, please check if Detail Amount, Pre-Freight Amount and Total Tax are updated automatically by changing the Invoice products.