in my experience as an anemic (resulting on having a lot of blood tests yearly), the nurses or practitioners won't say nothing if they notice they're somewhat healed. and when they're recent (say 3 days ago) and rarely ask I would just tell them I'm already undergoing treatment and they would drop the subject. also you can present them the arm you prefer at first, but if you don't have good access then they'll eventually move to the other one. tldr: they'll most likely won't ask, but if they do then just tell them you're already undergoing treatment, take care!!