The garlic will grow less big but the bulbs will store ok, I even plant cloves from rusty bulbs and they grow healthily if conditions in spring are not favourable to rust, soil conditions too, but some of it is that plants often get rust as they age. I would leave them growing a bit longer until say 2/3 of leaves are mostly yellow, then harvest.
I am unsure if garlic and leek rust are same family, sounds risky but in wet summers leeks rarely get rust here so watering helps them (too late for the garlic though).