Remove Constant Speck From 1080p Video

I have a 1080p video that runs for five minutes, and throughout the entire clip a tiny white speck sits on the subject’s jacket. I need that distraction removed cleanly so the jacket looks completely natural from first frame to last... (Budget: $30 - $250 USD, Jobs: After Effects, Animation, Photoshop, Video Editing, Video Post-editing, Video Processing, Video Production)