Couldn't remove it from my wife's account. And in her security settings, under Mobile Phone, it just showed her normal number. I talked to a surprisingly knowledgeable rep last night who said the setup feature was giving others a message that their number was already used (she had a bulletin to that effect). And that I should wait a while.
Sadly, it was still doing it this morning. In the meantime, though, I discovered that even logging into my account, going to Security settings, and trying to add the mobile number--that number couldn't be added there, either. Which sounded like a much more simple thing for them to check and fix.
So, back on the phone to Amazon I went, only I just told them about THAT problem with the ADD MOBILE feature, and he quickly "released" the number that he said "must have been used by someone else". (Though I knew it was probably somehow stuck in some Amazon setting cache somewhere after I had added it to my wife's account, even though I re-added her correct number back in later. But I didn't go into all that.).
That immediately fixed my Alexa App problem - it didn't even prompt me for the number - and now I can make calls(!) Looks like that Mobile number association in your account is what's used--and if you've set it, you won't even be prompted when adding the Voice Feature to the App. If you -can't- set it, you have a problem but one Amazon can probably quickly fix without getting Alexa mixed up in it.