Thank you--customer care resolved the question! Here it is. Yes, it was the issue you recommended about List, Customers, payment terms, etc. However, I was then testing that by viewing the most recent invoice I sent. In fact, there were 2 considerations

1. Making sure the payment terms were not "no terms" (which I thought meant "they can pay whenever they want" but instead means "default to due as of the date of the invoice"). I chose 31 days grace period just to have something more like what I actually do.

2. The view of the invoice which does not have on the screen the red "Past Due" would not take place until I started a new invoice after the date of the change in terms. So the reason I could not "make it go away" was because the terms were not officially "changed." In the future, unless the balance is, in fact, older than 31 days, I will not see the red Past Due on my screen--

That resolves the issue.

Thank you all.