Touche, Vern, although I challenge the claim of only three possible answers. I propose a fourth:
1) Yes, the work was performed under a task order
2) No, the work was performed under a task order
3) I don't know, because I don't know what work was performed, or
4) I don't know, because I don't know what "under a Task Order" means vs. "not under a Task Order"
If the answer's 3, I can go back and find out what the work was, when, etc. If the answer's 4, I can stick my head out and ask the Wifcon message board, fully prepared for the consequences of asking what may be an ill-informed question.
I think my answer is a combination of 3 and 4. I don't know if the work was performed under a Task Order, partially because I don't know what it means for work to be performed "under a Task Order." On my side, I'm going back to get a better understanding of when, what, where, how, etc. On the asking Wifcon side, I think we've come full circle back to my original question, which is, with the benefit of what I've learned from the comments and my research from what's been suggested:
"What does it mean for work to be performed under a Task Order?" If a contracting officer writes: "do tasks x, y, and z," is that a task order, because the contracting officer ordered the contractor to perform a task, or is it only a Task Order if there's a signed "Optional Form 347". Or, to perhaps oversimplify, "what's a Task Order?"
Again, I do appreciate all the help. I've gone through the FAR and the contract starting with 52.216-18, and gone back to the technical manager, and reviewed the invoices, contract file, and everything else based on what I've heard here.