بسم الله الرحمن الرحيم
If the blood removed by the syringe was not enough to flow then the wudhu will not break, but if the blood was in such a large amount that it would have flowed from its spot then the wudhu will break.
أفضل التطبيق العصري على مسائل القدوري
للمفتي محمد أشرف الاشاعتي
Vol.1 Pg.106