There was no movie adaptation of "The Scarlet Letter" released in 1908. The first film adaptation of Nathaniel Hawthorne's novel was released in 1917, starring
Pauline Frederick as Hester Prynn and
Wallace Reid as Arthur Dimmesdale.
While there were some silent films made in 1908, "The Scarlet Letter" wasn't one of them. It's possible you may be thinking of another film from that era.