The Woman in Red (or the Woman in the Red Dress) is a simulated character and notable feature in the Agent training program.
Meant to appear harmless but to catch trainees' attention. She is the only character in the program's city street setting wearing a vibrant shade of red. (In contrast, other pedestrians' attire is mostly black.) She makes eye contact with the subject and smiles flirtatiously upon crossing paths, then transforms into a simulated Agent, armed and dangerous. The lesson of the program is that any Bluepill can be overwritten by an Agent with little or no warning in the Matrix.
Mouse claims design credit for the Woman in Red and appears quite partial to her. He says "she doesn't talk much" but is available to meet interested parties of his choosing in a "more personalized milieu."
When in the Matrix, Mouse also carries a signed poster of the Woman in Red and ogles it on at least one occasion when he's alone.