What should someone do who has had a tooth surgically extracted and placed a cotton ball to stop the bleeding; should they pray in that state, or remove it to recite properly?

If the cotton does not prevent recitation, then there is no harm in praying with it. If it does prevent the articulation of letters and its removal does not cause harm, then it must be removed. However, if it prevents him and causes him harm, then he should pray and recite in the condition that enables him to recite.