I think you have to speak with her. The problem is she thinks she is being kind and that you do not feed your cat enough. You have to convince her that you love your cat, that the cat's diet is part of the vet's instructions, and that additional food will prevent his medication from working which would make him poorly and uncomfortable.
She might deny an accusation. Perhaps say, 'we love Mr Tiddles and we are concerned about his diabetes and have strict instructions from the vet not to over-feed him and to make sure he gets his diabetes tablets. Recently he's been throwing up and the tablets the vet prescribed for Mr Tiddles's health will have been in his vomit and so he won't have been getting the benefit of them. We don't want to prevent him from leaving the house, because he would hate that, and we care about his wellbeing as well as his physical health. Do you know of anyone in the neighbourhood who might have been feeding him half chickens and cat food pouches? I know it can't have been you because we discussed this previously and you promised to cooperate with us.'
Does your neighbour have pets? Is there a particular reason why she wants to provide for your cat?