[David L.]

The invoice will be accompanied by a bill of quantities or a list of works performed.

Firstly, the 'invoice' = a list of goods sent or services provided, with a statement of the sum due for these; a bill.

So you will see, it sounds odd accounting practice to send an invoice and 'accompany this with a bill'.

"The invoice will itemize materials used, or works performed."
In this context, where the contractor has various elements of the job eg put pond in ground and correctly align; install plumbing to pond; lay gravel around pond etc, 'works' is appropriate.

Federal Dpartment of Works
Inspection and Restoration Works Performed after the Niigata-Chuetsu-Oki Earthquake (March 13th) ..
The following is a list of works performed by the Society over the past few decades.
Programmes of major works performed by SHEFFIELD ORATORIO CHORUS