... when I sent her an invite to the io group, she says it tells herShe's probably confused about her email addresses.
If the address you invited were in fact already on the group's Members list then the Invite page would tell you that, and not send the invitation.
She might be on your group's Members list under another email address though, and that may be why she believes she's already a member.
If she tried to accept the invitation while already logged in to Groups.io under an alternate email address that may have produced the confusion.
Or... It may be telling her that she already has an account at Groups.io, and she's confused that for being a member of your group. But accepting an invitation wouldn't bother to tell you that, she must have tried to use the "sign up" link to create a new account instead.
I would suggest that you send her a new invitation, and instruct her to simply reply by email rather than click on anything in the invitation. That will get her email address on your group's Members list, and then you can sort out logging into Groups.io later.
Is there a way I can just add her?Only if you upgrade the group to Premium. You can do that for a single month, automatically reverting to Basic at the end of the month, for a one-time $10 fee.