All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
These cotton threads that stick to a wound when wearing socks create a barrier that undoubtedly prevents water from reaching the skin beneath them. Therefore, it is obligatory to remove them before performing Wudu (ablution), unless doing so would cause you harm.
Allah knows best.