A 23-year-old female maid was making a bed in a hotel bedroom. As she straightened the sheet by running her right hand over the surface with her fingers extended, she caught the end of the index finger in a fold. She experienced a sudden, severe pain over the base of the terminal phalanx. Several hours later when the pain had diminished, she noted that the end of her right index finger was swollen and she could not completely extend the terminal interphalangeal joint. Which one of the following structures within the digit was most likely injured?