My conversation went along the lines of:-
BA. You know you have used all your partner cards this year?
Me. Yes. This is regarding a card I gifted last year.
BA. But you don’t have any cards to gift this year (proceeds to read out the people I have gifted them to this year).
Me. Yes I know, this is regarding last year (explain the rule again).
BA. Reads the rule out loud and says my Mum has had a full year of membership.
Me. No she hasn’t. She had the remainder of her current year which was about 11.5 months. She should now have the following year.
BA. You know you have no more partner cards to gift this year?

Repeat the above for 30 minutes. Explained it was a known IT issue. Walked very slowly through the chronology of the actual dates and how that aligns to the rules.

Oh oh yes and this bit:-
Me. If her membership renewal date is the 8th May and I gift the card on the 20th May. When does the remainder of her current membership year expire?
BA. December.
Me. Why do you think that? That is not her membership year, it is the calendar year.

She was lovely, but it would have got heated on both sides if we carried on so it was time to ask for it to be referred!