How in the Order of Phoenix is that when Umbridge holds Harry's hand in detention, his scar hurts? She is not wearing the horcroux yet.

anyone can get a headache looking at umbridge

It hurts because of Voldemort. Umbridge touching his hand at the same time is just a coincidence.

Ill timing. She grabbed his hand right as Voldemort felt a particularly strong surge of emotion. And when Voldemort felt strong emotions, Harry's scar would hurt.

Umbridge touches Harry at the exact moment Voldemort feels a strong emotion. The fact that it is Umbridge touching Harry is complete coincidence.