Sorry I didn't know that you didn't know how oyster cards work.
Again, I don't think cockatoo can ask her to top up out of her own money and then reimburse her. So I don't think the au pair should sub cockatoo. I think that ideally you'd have a situation where there was always enough on the Oyster to cover work journeys but the au pair could be in charge of managing her expenses. But this is clearly too complex a situation for that.
And I think the nitpicking comes from being a short of cash. I'd nitpick then too, tbh.
I am not insistent that she is fiddling expenses, as in, on purpose (if that was to me). I absolutely accept perhaps it's an oversight on her part, rather than deliberate.
In any event, the au pair seems to be claiming an expense needlessly, which might be accidental or she's not thought it through. Technically she's claiming what she's not spent. So in that sense it's fiddling, she could just not be paying attention etc.
If it were me, I'd shrug it off and assume the au pair was making 4 bus journeys and for the sake of a few quid, not bring it up (though I'd roll my eyes and probably grr my teeth a bit too, I'd look like this
) Anyway, it would irk me but I could afford to bump up the Oyster expenditure.