You can use the note pad in the T&M invoice printing window (3-10-3).  You may have to add that note field to the invoice "report form".

You will need to update that note pad for each billing since it would apply to any invoice you print. 

Or you can create a custom pop up field to enter the scope but that won't be saved anywhere.  So make sure whatever you do, you create a pdf in case you need to reprint in the future.

I would use a field on the job record (like the note) and pull it into the T&M invoice report