Impasse with Hotmail/Outlook account re-verification

I'm not able to access my Hotmail account due to dilemma.

Every few months, when I'm logging in, there's a pop-up asking me to re-confirm, yet again, the alternative email I gave them as a link. This is probably the single most aggravating annoyance, because the alternative is something I don't use, and half the time it's a chore to track down the password or, worse, re-constitute the account.

Hotmail/Outlook gives you two choices with the pop-up, something like:
- Looks good!
- No, I don't have that anymore.

In the past, when I click "Looks good!" seems to me that's always been the end. It doesn't ask further.

But now I'm stuck with something where I really can't access the linked account and I'm not sure what to do.  I can either pretend that it's okay, hope it goes through, and then change the account it's linked to.  Or I can truthfully say I don't have it any more ... but then I don't know what will happen, whether I'll lose access entirely, or just be offered the opportunity to use a different link.  Or, better still, not have to bother with a verification link at all.

Anyone familiar with this problem?